Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
212 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 99 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×Q8×C29 | C2 |
| prime radical | C2×D116 | C22 |
| hypercenter | C4×Q8 | D29 |
| hypocenter | C29 | #556 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×Q8×C29 | C2 | semidirect |
| 2. #11745308 | C2 | semidirect |
| 3. #11745260 | C2 | semidirect |
| 4. #11745254 | C2 | semidirect |
| 7. #11745231 | C2 | semidirect |
| 8. C4×Dic58 | C2 | semidirect |
| 58. C4×Q8 | D29 | semidirect |
| 61. C29 | #556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C29 | 2 |
| #11745308 | 2 |
| #11745260 | 2 |
| #11745254 | 2 |
| #11745237 | 2 |
| C4×D116 | 2 |
| #11745231 | 2 |
| C4×Dic58 | 2 |
| #556 | 29 |