Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
948 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 171 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 | #392×C71 | C2 |
| hypercenter | #392 | D71 |
| hypocenter | C71 | #2541 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556124 | C2 | semidirect |
| 2. C2×#14556124 | C2 | semidirect |
| 3. C2×#14556101 | C2 | semidirect |
| 4. C2×#14556100 | C2 | semidirect |
| 5. C2×(C22⋊D71)⋊C4 | C2 | semidirect |
| 6. #17985909 | C2 | semidirect |
| 7. #17985908 | C2 | semidirect |
| 8. #17985907 | C2 | semidirect |
| 9. #17985899 | C2 | semidirect |
| 10. #17985850 | C2 | semidirect |
| 11. #392×C71 | C2 | semidirect |
| 61. C2×C22⋊D71 | D4 | semidirect |
| 71. Dic71⋊C4 | D4 | semidirect |
| 77. C4×Dic71 | D4 | semidirect |
| 177. Dic71 | #121 | semidirect |
| 178. Dic71 | #127 | semidirect |
| 189. C71 | #2541 | semidirect |
| 198. #392 | D71 | semidirect |