Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
290 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 107 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 | C4×D4×C29 | C2 |
| hypercenter | C4×D4 | D29 |
| hypocenter | C29 | #548 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90805 | C2 | semidirect |
| 2. C22×Dic58 | C2 | semidirect |
| 3. C4×D4×C29 | C2 | semidirect |
| 4. #11745301 | C2 | semidirect |
| 5. #11745292 | C2 | semidirect |
| 6. #11745286 | C2 | semidirect |
| 7. #11745258 | C2 | semidirect |
| 8. #11745247 | C2 | semidirect |
| 9. #11745243 | C2 | semidirect |
| 10. #11745237 | C2 | semidirect |
| 11. C4×Dic58 | C2 | semidirect |
| 58. Dic58 | D4 | semidirect |
| 64. C22×C29 | #41 | semidirect |
| 94. C4×D4 | D29 | semidirect |
| 95. C29 | #548 | semidirect |
| 151. C22 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90805 | 2 |
| C22×Dic58 | 2 |
| C4×D4×C29 | 2 |
| #11745301 | 2 |
| #11745292 | 2 |
| #11745286 | 2 |
| #11745258 | 2 |
| #11745247 | 2 |
| #11745243 | 2 |
| #11745237 | 2 |
| C4×Dic58 | 2 |
| #548 | 29 |