Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
312 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 312 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×D29 |
| commutator, socle, cosocle | C22×C29 | C24 |
| Fitting | C29×#121 | C2 |
| hypercenter | #121 | D29 |
| hypocenter | C29 | #550 |
| 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. #11745302 | C2 | semidirect |
| 5. #11745302 | C2 | semidirect |
| 6. #11745301 | C2 | semidirect |
| 7. C4×C22⋊D29 | C2 | semidirect |
| 8. #11745257 | C2 | semidirect |
| 9. #11745249 | C2 | semidirect |
| 10. #11745246 | C2 | semidirect |
| 11. #11745243 | C2 | semidirect |
| 61. Dic58 | D4 | semidirect |
| 81. Dic29 | #41 | semidirect |
| 97. #121 | D29 | semidirect |
| 101. C29 | #550 | 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 |
| #11745302 | 2 |
| #11745301 | 2 |
| C4×C22⋊D29 | 2 |
| #11745257 | 2 |
| #11745249 | 2 |
| #11745246 | 2 |
| #11745243 | 2 |
| #550 | 29 |