Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
222 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 111 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×C4⋊Q8 | C2 |
| prime radical | C22×D29 | C23 |
| hypercenter | C4⋊Q8 | D29 |
| hypocenter | C29 | #533 |
| 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. C29×C4⋊Q8 | C2 | semidirect |
| 3. Q8×Dic29 | C2 | semidirect |
| 6. #11745252 | C2 | semidirect |
| 7. #11745249 | C2 | semidirect |
| 9. #11745231 | C2 | semidirect |
| 39. C4×D29 | Q8 | semidirect |
| 59. C4⋊Q8 | D29 | semidirect |
| 67. C29 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×C4⋊Q8 | 2 |
| #11745308 | 2 |
| Q8×Dic29 | 2 |
| #11745259 | 2 |
| #11745254 | 2 |
| #11745252 | 2 |
| #11745249 | 2 |
| C42×D29 | 2 |
| #11745231 | 2 |
| #533 | 29 |