Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1840 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 685 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×C22⋊C4×C71 | C2 |
| socle | C24×C71 | C23 |
| hypercenter | C22×C22⋊C4 | D71 |
| hypocenter | C71 | C22×C22⋊Q8 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic142 | C2 | semidirect |
| 3. C2×#14556105 | C2 | direct (N × H) |
| 4. C22×C4⋊Dic71 | C2 | semidirect |
| 5. C22×Dic71⋊C4 | C2 | semidirect |
| 6. C22×Dic71⋊C4 | C2 | semidirect |
| 10. C22×Dic142 | C22 | semidirect |
| 17. #14556105 | C22 | direct (N × H) |
| 18. C2×C4⋊Dic71 | C22 | semidirect |
| 19. C2×Dic71⋊C4 | C22 | semidirect |
| 20. C2×Dic71⋊C4 | C22 | semidirect |
| 27. C2×Dic142 | C23 | semidirect |
| 38. C4⋊Dic71 | C23 | semidirect |
| 39. Dic71⋊C4 | C23 | semidirect |
| 40. Dic71⋊C4 | C23 | semidirect |
| 44. C24×C71 | Q8 | semidirect |
| 57. C23×C71 | C2×Q8 | semidirect |
| 78. C22×C71 | C22⋊Q8 | semidirect |
| 81. C22×C71 | C22×Q8 | semidirect |
| 91. C2×C71 | C2×C22⋊Q8 | semidirect |
| 96. C71 | C22×C22⋊Q8 | semidirect |
| 124. C24 | Dic142 | semidirect |
| 153. C23 | C2×Dic142 | semidirect |
| 174. C22 | #14556105 | direct (N × H) |
| 177. C22 | C22×Dic142 | semidirect |
| 187. C2 | C2×#14556105 | direct (N × H) |