Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D467 |
| commutator, socle, cosocle | C22×C467 | C24 |
| Fitting | #123×C467 | C2 |
| prime radical | #28417921 | C2 |
| hypercenter | #123 | D467 |
| hypocenter | C467 | #551 |
| LCS | G ▷ C22×C467 ▷ C467 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28417948 | C2 | semidirect |
| 2. #28417948 | C2 | semidirect |
| 3. #28417939 | C2 | semidirect |
| 4. #28417937 | C2 | semidirect |
| 5. #28417935 | C2 | semidirect |
| 6. #28417933 | C2 | semidirect |
| 7. #28417930 | C2 | semidirect |
| 9. D4×Dic467 | C2 | semidirect |
| 10. (C22⋊D467)⋊C4 | C2 | semidirect |
| 11. #28417912 | C2 | semidirect |
| 12. #28417911 | C2 | semidirect |
| 13. C2×(C2×D467)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D467 | C2 | semidirect |
| 15. #123×C467 | C2 | semidirect |
| 17. C2×Dic934 | C22 | semidirect |
| 21. C22×Dic467 | C22 | semidirect |
| 24. C4⋊Dic467 | C22 | semidirect |
| 25. C4⋊Dic467 | C22 | semidirect |
| 26. C4⋊Dic467 | C22 | semidirect |
| 27. C4⋊Dic467 | C22 | semidirect |
| 28. Dic467⋊C4 | C22 | semidirect |
| 29. Dic467⋊C4 | C22 | semidirect |
| 32. C22⋊Dic467 | C22 | semidirect |
| 41. C4×Dic467 | C22 | semidirect |
| 42. C4×Dic467 | C22 | semidirect |
| 43. C4×Dic467 | C22 | semidirect |
| 46. C4⋊C4×C467 | C22 | semidirect |
| 47. C4⋊C4×C467 | C22 | semidirect |
| 49. C22⋊C4×C467 | C22 | semidirect |
| 50. C22⋊C4×C467 | C22 | semidirect |
| 110. C467 | #551 | semidirect |
| 117. #123 | D467 | semidirect |
| 143. C4⋊C4 | C2×D467 | semidirect |
| 144. C4⋊C4 | C2×D467 | semidirect |
| 157. C22⋊C4 | C2×D467 | semidirect |
| 158. C22⋊C4 | C2×D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28417948 | 2 |
| #28417939 | 2 |
| #28417937 | 2 |
| #28417935 | 2 |
| #28417933 | 2 |
| #28417930 | 2 |
| #28417921 | 2 |
| D4×Dic467 | 2 |
| (C22⋊D467)⋊C4 | 2 |
| #28417912 | 2 |
| #28417911 | 2 |
| C2×(C2×D467)⋊C4 | 2 |
| C22⋊C4×D467 | 2 |
| #123×C467 | 2 |
| #551 | 467 |