Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
236 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 236 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×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×#123 | C2 |
| prime radical | #11745302 | C2 |
| hypercenter | #123 | D29 |
| hypocenter | C29 | #559 |
| 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 |
| 3. #11745297 | C2 | semidirect |
| 4. C4×C22⋊D29 | C2 | semidirect |
| 5. #11745256 | C2 | semidirect |
| 6. #11745249 | C2 | semidirect |
| 7. #11745247 | C2 | semidirect |
| 8. #11745247 | C2 | semidirect |
| 9. #11745243 | C2 | semidirect |
| 73. #123 | D29 | semidirect |
| 77. C29 | #559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#123 | 2 |
| #11745302 | 2 |
| #11745297 | 2 |
| C4×C22⋊D29 | 2 |
| #11745256 | 2 |
| #11745249 | 2 |
| #11745247 | 2 |
| #11745243 | 2 |
| #559 | 29 |