Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
924 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 189 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 | #390×C71 | C2 |
| hypercenter | #390 | D71 |
| hypocenter | C71 | #2856 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556124 | C2 | semidirect |
| 2. C2×#14556103 | C2 | semidirect |
| 3. C2×#14556101 | C2 | semidirect |
| 4. C2×#14556099 | C2 | semidirect |
| 5. C2×C42×D71 | C2 | semidirect |
| 6. #17985901 | C2 | semidirect |
| 7. #17985899 | C2 | semidirect |
| 8. #17985868 | C2 | semidirect |
| 9. #390×C71 | C2 | semidirect |
| 51. C2×C4×D71 | D4 | semidirect |
| 52. C2×C4×D71 | D4 | semidirect |
| 59. C4×Dic71 | D4 | semidirect |
| 128. C2×D71 | #127 | semidirect |
| 131. C4×C71 | #121 | semidirect |
| 134. Dic71 | #121 | semidirect |
| 144. C71 | #2856 | semidirect |
| 152. #390 | D71 | semidirect |
| 278. C4 | #14556101 | semidirect |