Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
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×D457 |
| commutator, socle, cosocle | C22×C457 | C24 |
| Fitting | #123×C457 | C2 |
| hypercenter | #123 | D457 |
| hypocenter | C457 | #547 |
| LCS | G ▷ C22×C457 ▷ C457 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20300741 | C2 | semidirect |
| 2. C2×#20300740 | C2 | semidirect |
| 3. #28410551 | C2 | semidirect |
| 4. #28410537 | C2 | semidirect |
| 5. #28410536 | C2 | semidirect |
| 6. #28410534 | C2 | semidirect |
| 7. #28410530 | C2 | semidirect |
| 8. #28410529 | C2 | semidirect |
| 9. #28410525 | C2 | semidirect |
| 10. #28410524 | C2 | semidirect |
| 11. #28410512 | C2 | semidirect |
| 12. #28410512 | C2 | semidirect |
| 13. C2×#20300720 | C2 | semidirect |
| 14. C4⋊C4×D457 | C2 | semidirect |
| 15. #123×C457 | C2 | semidirect |
| 61. C22⋊D457 | D4 | semidirect |
| 107. Dic457 | #41 | semidirect |
| 115. C457 | #547 | semidirect |
| 123. #123 | D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300741 | 2 |
| C2×#20300740 | 2 |
| #28410551 | 2 |
| #28410537 | 2 |
| #28410536 | 2 |
| #28410534 | 2 |
| #28410530 | 2 |
| #28410529 | 2 |
| #28410525 | 2 |
| #28410524 | 2 |
| #28410512 | 2 |
| C2×#20300720 | 2 |
| C4⋊C4×D457 | 2 |
| #123×C457 | 2 |
| #547 | 457 |