Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #126×C457 | C2 |
| prime radical | C2×C22⋊D457 | C22 |
| hypercenter | #126 | D457 |
| hypocenter | C457 | #563 |
| LCS | G ▷ C22×C457 ▷ C457 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28410552 | C2 | semidirect |
| 2. #28410551 | C2 | semidirect |
| 3. #28410547 | C2 | semidirect |
| 4. #28410546 | C2 | semidirect |
| 5. #28410545 | C2 | semidirect |
| 6. #28410543 | C2 | semidirect |
| 7. #28410542 | C2 | semidirect |
| 11. #28410532 | C2 | semidirect |
| 12. #28410530 | C2 | semidirect |
| 13. #28410529 | C2 | semidirect |
| 14. #28410529 | C2 | semidirect |
| 15. #126×C457 | C2 | semidirect |
| 97. C457 | #563 | semidirect |
| 104. #126 | D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28410552 | 2 |
| #28410551 | 2 |
| #28410547 | 2 |
| #28410546 | 2 |
| #28410545 | 2 |
| #28410543 | 2 |
| #28410542 | 2 |
| #28410538 | 2 |
| #28410536 | 2 |
| #28410534 | 2 |
| #28410532 | 2 |
| #28410530 | 2 |
| #28410529 | 2 |
| #126×C457 | 2 |
| #563 | 457 |