Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
270 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 270 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 | C22×Q8×C29 | C2 |
| prime radical | C2×#90805 | C2 |
| hypercenter | C22×Q8 | D29 |
| hypocenter | C29 | #536 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q8×C29 | C2 | semidirect |
| 3. #11745309 | C2 | semidirect |
| 4. #11745308 | C2 | semidirect |
| 5. #11745306 | C2 | semidirect |
| 6. #11745291 | C2 | semidirect |
| 7. #11745288 | C2 | semidirect |
| 54. C22×Q8 | D29 | semidirect |
| 60. C29 | #536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C29 | 2 |
| C2×#90805 | 2 |
| #11745309 | 2 |
| #11745308 | 2 |
| #11745306 | 2 |
| #11745291 | 2 |
| #11745288 | 2 |
| #536 | 29 |