Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| hypercenter | #123 | D467 |
| hypocenter | C467 | #547 |
| 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. C2×#21418743 | C2 | semidirect |
| 2. C2×#21418742 | C2 | semidirect |
| 3. #28417952 | C2 | semidirect |
| 4. #28417938 | C2 | semidirect |
| 5. #28417937 | C2 | semidirect |
| 6. #28417935 | C2 | semidirect |
| 7. #28417931 | C2 | semidirect |
| 8. #28417930 | C2 | semidirect |
| 9. #28417926 | C2 | semidirect |
| 10. #28417925 | C2 | semidirect |
| 11. (C22⋊D467)⋊C4 | C2 | semidirect |
| 12. (C22⋊D467)⋊C4 | C2 | semidirect |
| 13. C2×Dic467⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D467 | C2 | semidirect |
| 15. #123×C467 | C2 | semidirect |
| 61. C22⋊D467 | D4 | semidirect |
| 107. Dic467 | #41 | semidirect |
| 115. C467 | #547 | semidirect |
| 123. #123 | D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21418743 | 2 |
| C2×#21418742 | 2 |
| #28417952 | 2 |
| #28417938 | 2 |
| #28417937 | 2 |
| #28417935 | 2 |
| #28417931 | 2 |
| #28417930 | 2 |
| #28417926 | 2 |
| #28417925 | 2 |
| (C22⋊D467)⋊C4 | 2 |
| C2×Dic467⋊C4 | 2 |
| C4⋊C4×D467 | 2 |
| #123×C467 | 2 |
| #547 | 467 |