Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D467 |
| commutator, socle, cosocle | C22×C467 | C24 |
| Frattini | C22 | C23×D467 |
| Fitting | C23×C4×C467 | C2 |
| hypercenter | C23×C4 | D467 |
| hypocenter | C467 | #525 |
| LCS | G ▷ C22×C467 ▷ C467 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#21418743 | C2 | semidirect |
| 2. #28417936 | C2 | semidirect |
| 3. #28417932 | C2 | semidirect |
| 4. #28417927 | C2 | semidirect |
| 5. #28417922 | C2 | semidirect |
| 6. C4×C22⋊D467 | C2 | semidirect |
| 7. #28417912 | C2 | semidirect |
| 8. C23×C4×C467 | C2 | semidirect |
| 10. C2×Dic934 | C22 | semidirect |
| 11. C2×D1868 | C22 | semidirect |
| 14. C2×C4×D467 | C22 | semidirect |
| 15. C4⋊Dic467 | C22 | semidirect |
| 16. Dic467⋊C4 | C22 | semidirect |
| 19. (C2×D467)⋊C4 | C22 | semidirect |
| 20. C4×Dic467 | C22 | semidirect |
| 42. C2×C4×C467 | D4 | semidirect |
| 51. C22×C467 | #41 | semidirect |
| 65. C467 | #525 | semidirect |
| 68. C23×C4 | D467 | semidirect |
| 108. C2×C4 | C22⋊D467 | semidirect |
| 119. C22 | #21418743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21418743 | 2 |
| #28417936 | 2 |
| #28417932 | 2 |
| #28417927 | 2 |
| #28417922 | 2 |
| C4×C22⋊D467 | 2 |
| #28417912 | 2 |
| C23×C4×C467 | 2 |
| #525 | 467 |