Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1348 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 193 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 | #2433 |
| 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. C22×D4×D71 | C2 | semidirect |
| 2. C2×#14556125 | C2 | semidirect |
| 3. C2×#14556124 | C2 | semidirect |
| 4. C2×#14556103 | C2 | semidirect |
| 5. C2×#14556098 | C2 | semidirect |
| 6. #17985908 | C2 | semidirect |
| 7. #17985900 | C2 | semidirect |
| 8. C4×(C2×D71)⋊C4 | C2 | semidirect |
| 9. #390×C71 | C2 | semidirect |
| 13. C22×D284 | C22 | semidirect |
| 14. C22×D284 | C22 | semidirect |
| 16. C22×C22⋊D71 | C22 | semidirect |
| 26. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 27. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 28. C2×C4×Dic71 | C22 | semidirect |
| 29. C71⋊#95 | C22 | semidirect |
| 31. C2×C4⋊C4×C71 | C22 | semidirect |
| 32. C2×C22⋊C4×C71 | C22 | semidirect |
| 33. C2×C42×C71 | C22 | semidirect |
| 52. C2×D284 | D4 | semidirect |
| 64. C2×C4×D71 | D4 | semidirect |
| 67. (C2×D71)⋊C4 | D4 | semidirect |
| 72. C2×D4×C71 | D4 | semidirect |
| 113. C2×C4×C71 | C2×D4 | semidirect |
| 121. C2×Dic71 | C2×D4 | semidirect |
| 152. C2×D71 | #127 | semidirect |
| 155. C4×C71 | #120 | semidirect |
| 168. C71 | #2433 | semidirect |
| 176. #390 | D71 | semidirect |
| 194. C2×C4⋊C4 | C2×D71 | semidirect |
| 198. C2×C22⋊C4 | C2×D71 | semidirect |
| 200. C2×C42 | C2×D71 | semidirect |
| 231. C2×D4 | D284 | semidirect |
| 293. C2×C4 | D4×D71 | semidirect |
| 325. C4 | #14556098 | semidirect |