Finite Group DatabasebetaFinite Group DatabasebetaOrder 8896.
202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 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 | C22×D139 |
| commutator, socle | C23×C139 | C23 |
| Fitting | #95×C139 | C2 |
| hypercenter | #95 | D139 |
| hypocenter | C139 | #393 |
| LCS | G ▷ C23×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic278 | C2 | semidirect |
| 4. C139⋊#95 | C2 | semidirect |
| 5. #95×C139 | C2 | semidirect |
| 19. C22×D139 | Q8 | semidirect |
| 52. C139 | #393 | semidirect |
| 58. #95 | D139 | semidirect |