Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 605 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D71 |
| commutator | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C22×C4⋊C4×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C22×C4⋊C4 | D71 |
| hypocenter | C71 | C22×#123 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C4×D71 | C2 | semidirect |
| 3. C2×#14556113 | C2 | direct (N × H) |
| 4. C22×Dic71⋊C4 | C2 | semidirect |
| 5. C22×(C2×D71)⋊C4 | C2 | semidirect |
| 6. C22×(C2×D71)⋊C4 | C2 | semidirect |
| 7. C22×(C2×D71)⋊C4 | C2 | semidirect |
| 8. C22×C4⋊C4×C71 | C2 | semidirect |
| 16. C22×C4×D71 | C22 | semidirect |
| 17. #14556113 | C22 | direct (N × H) |
| 18. C2×Dic71⋊C4 | C22 | semidirect |
| 19. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 20. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 25. C2×C4⋊C4×C71 | C22 | semidirect |
| 41. C2×C4×D71 | C23 | semidirect |
| 42. Dic71⋊C4 | C23 | semidirect |
| 43. (C2×D71)⋊C4 | C23 | semidirect |
| 44. (C2×D71)⋊C4 | C23 | semidirect |
| 45. (C2×D71)⋊C4 | C23 | semidirect |
| 53. C4⋊C4×C71 | C23 | semidirect |
| 80. C22×C71 | #123 | semidirect |
| 98. C2×C71 | C2×#123 | semidirect |
| 105. C71 | C22×#123 | semidirect |
| 110. C22×C4⋊C4 | D71 | semidirect |
| 127. C2×C4⋊C4 | C2×D71 | semidirect |
| 155. C4⋊C4 | C22×D71 | semidirect |
| 193. C22 | #14556113 | direct (N × H) |
| 205. C2 | C2×#14556113 | direct (N × H) |