Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
656 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C2×C71 | C22×C42 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | C2×#97×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C2×#97 | D71 |
| hypocenter | C71 | C2×C4×M16 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #17985951 | C2 | direct (N × H) |
| 4. C2×#14556039 | C2 | semidirect |
| 5. C2×C8×Dic71 | C2 | semidirect |
| 6. C2×#97×C71 | C2 | semidirect |
| 9. C2×#11765848 | C4 | semidirect |
| 16. #14556039 | C22 | semidirect |
| 17. C8×Dic71 | C22 | semidirect |
| 20. #97×C71 | C22 | semidirect |
| 29. #11765848 | C2×C4 | semidirect |
| 30. C2×C71⋊C8 | C2×C4 | semidirect |
| 37. C2×C8×C71 | C2×C4 | semidirect |
| 51. C2×Dic71 | M16 | semidirect |
| 57. C8×C71 | C22×C4 | semidirect |
| 58. C71⋊C8 | C22×C4 | semidirect |
| 69. Dic71 | C2×M16 | semidirect |
| 70. C2×C71 | C4×M16 | semidirect |
| 75. C71 | C2×C4×M16 | semidirect |
| 80. C2×#97 | D71 | semidirect |
| 94. #97 | C2×D71 | semidirect |
| 109. C2×C8 | C4×D71 | semidirect |
| 133. C8 | C2×C4×D71 | semidirect |
| 146. C2 | #17985951 | direct (N × H) |