Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
352 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D7 |
| commutator, socle, prime radical, cosocle | C23×C7 | C24 |
| Fitting | C7×#401 | C2 |
| hypercenter | #401 | D7 |
| hypocenter | C7 | #2645 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #401 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 111. C7 | #2645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#401 | 2 |
| C7⋊#401 | 2 |
| #89432 | 2 |
| #89431 | 2 |
| #89420 | 2 |
| #89419 | 2 |
| #89418 | 2 |
| #2645 | 7 |