Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D71 |
| commutator | C22×C71 | C2×C42 |
| Fitting | C2×#97×C71 | C2 |
| socle | C23×C71 | C22×C4 |
| hypercenter | C2×#97 | D71 |
| hypocenter | C71 | #1749 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#14556039 | C2 | semidirect |
| 4. #17985753 | C2 | semidirect |
| 5. C2×#97×C71 | C2 | semidirect |
| 13. (C2×D71)⋊C8 | C4 | semidirect |
| 30. C2×C71⋊C8 | C2×C4 | semidirect |
| 38. C2×C8×C71 | C2×C4 | semidirect |
| 74. C2×D71 | #97 | semidirect |
| 87. C71 | #1749 | semidirect |
| 91. C2×#97 | D71 | semidirect |
| 122. C2×C8 | C4×D71 | semidirect |