Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
588 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 249 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 | C22×C71 | C23×C4 |
| Fitting | #384×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #384 | D71 |
| hypocenter | C71 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. #14556128 | C4 | semidirect |
| 35. C4×Dic71 | Q8 | semidirect |
| 69. C4×C71 | C4×Q8 | semidirect |
| 73. Dic71 | C4⋊Q8 | semidirect |
| 80. C71 | C4×C4⋊Q8 | semidirect |
| 153. C4 | #14556093 | semidirect |