Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 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×#121 | C2 |
| hypercenter | #121 | D29 |
| hypocenter | C29 | #537 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90807 | C2 | semidirect |
| 2. C2×#90805 | C2 | semidirect |
| 3. C29×#121 | C2 | semidirect |
| 4. #11745301 | C2 | semidirect |
| 5. #11745300 | C2 | semidirect |
| 6. #11745300 | C2 | semidirect |
| 7. #11745286 | C2 | semidirect |
| 8. #11745259 | C2 | semidirect |
| 9. C4⋊C4×D29 | C2 | semidirect |
| 10. #11745246 | C2 | semidirect |
| 11. #11745240 | C2 | semidirect |
| 59. C4×D29 | D4 | semidirect |
| 99. #121 | D29 | semidirect |
| 101. C29 | #537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90807 | 2 |
| C2×#90805 | 2 |
| C29×#121 | 2 |
| #11745301 | 2 |
| #11745300 | 2 |
| #11745286 | 2 |
| #11745259 | 2 |
| C4⋊C4×D29 | 2 |
| #11745246 | 2 |
| #11745240 | 2 |
| #537 | 29 |