Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
592 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #389×C71 | C2 |
| hypercenter | #389 | D71 |
| hypocenter | C71 | #2683 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556108 | C2 | semidirect |
| 2. C2×#14556106 | C2 | semidirect |
| 3. #17985921 | C2 | semidirect |
| 4. #17985921 | C2 | semidirect |
| 5. #17985920 | C2 | semidirect |
| 7. #17985897 | C2 | semidirect |
| 9. #389×C71 | C2 | semidirect |
| 39. C2×D284 | Q8 | semidirect |
| 49. C4⋊Dic71 | D4 | semidirect |
| 64. C4⋊C4×C71 | D4 | semidirect |
| 132. C71 | #2683 | semidirect |
| 140. #389 | D71 | semidirect |
| 191. C4⋊C4 | D284 | semidirect |