Finite Group DatabasebetaFinite Group DatabasebetaOrder 29888.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #121×C467 | C2 |
| hypercenter | #121 | D467 |
| hypocenter | C467 | #540 |
| LCS | G ▷ C22×C467 ▷ C467 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28417949 | C2 | semidirect |
| 2. #28417944 | C2 | semidirect |
| 3. #28417937 | C2 | semidirect |
| 4. #28417935 | C2 | semidirect |
| 5. #28417927 | C2 | semidirect |
| 6. #28417925 | C2 | semidirect |
| 7. #28417924 | C2 | semidirect |
| 8. D4×Dic467 | C2 | semidirect |
| 9. #28417915 | C2 | semidirect |
| 10. #28417912 | C2 | semidirect |
| 11. #121×C467 | C2 | semidirect |
| 79. C467 | #540 | semidirect |
| 88. #121 | D467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28417949 | 2 |
| #28417944 | 2 |
| #28417937 | 2 |
| #28417935 | 2 |
| #28417927 | 2 |
| #28417925 | 2 |
| #28417924 | 2 |
| D4×Dic467 | 2 |
| #28417915 | 2 |
| #28417912 | 2 |
| #121×C467 | 2 |
| #540 | 467 |