Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 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×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×#123 | C2 |
| hypercenter | #123 | D29 |
| hypocenter | C29 | #562 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#123 | C2 | semidirect |
| 2. #11745301 | C2 | semidirect |
| 3. #11745300 | C2 | semidirect |
| 4. #11745292 | C2 | semidirect |
| 5. #11745286 | C2 | semidirect |
| 6. #11745259 | C2 | semidirect |
| 7. #11745258 | C2 | semidirect |
| 8. #11745256 | C2 | semidirect |
| 9. #11745252 | C2 | semidirect |
| 10. #11745248 | C2 | semidirect |
| 11. #11745247 | C2 | semidirect |
| 12. #11745247 | C2 | semidirect |
| 13. #11745246 | C2 | semidirect |
| 14. #11745245 | C2 | semidirect |
| 15. #11745240 | C2 | semidirect |
| 116. #123 | D29 | semidirect |
| 125. C29 | #562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#123 | 2 |
| #11745301 | 2 |
| #11745300 | 2 |
| #11745292 | 2 |
| #11745286 | 2 |
| #11745259 | 2 |
| #11745258 | 2 |
| #11745256 | 2 |
| #11745252 | 2 |
| #11745248 | 2 |
| #11745247 | 2 |
| #11745246 | 2 |
| #11745245 | 2 |
| #11745240 | 2 |
| #562 | 29 |