Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
236 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 97 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×#124 | C2 |
| prime radical | #11745302 | C2 |
| hypercenter | #124 | D29 |
| hypocenter | C29 | #559 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#124 | C2 | semidirect |
| 2. #11745309 | C2 | semidirect |
| 3. Q8×Dic29 | C2 | semidirect |
| 5. D4×Dic29 | C2 | semidirect |
| 6. #11745248 | C2 | semidirect |
| 7. #11745247 | C2 | semidirect |
| 8. #11745245 | C2 | semidirect |
| 9. #11745243 | C2 | semidirect |
| 10. C4×D116 | C2 | semidirect |
| 11. C4×Dic58 | C2 | semidirect |
| 79. #124 | D29 | semidirect |
| 87. C29 | #559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#124 | 2 |
| #11745309 | 2 |
| Q8×Dic29 | 2 |
| #11745302 | 2 |
| D4×Dic29 | 2 |
| #11745248 | 2 |
| #11745247 | 2 |
| #11745245 | 2 |
| #11745243 | 2 |
| C4×D116 | 2 |
| C4×Dic58 | 2 |
| #559 | 29 |