Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
392 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 141 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×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #391×C71 | C2 |
| hypercenter | #391 | D71 |
| hypocenter | C71 | #2806 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 33. C2×Dic142 | Q8 | semidirect |
| 40. C4⋊Dic71 | Q8 | semidirect |
| 111. C71 | #2806 | semidirect |