Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
402 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Fitting | C8×Q8×C71 | C2 |
| hypercenter | C8×Q8 | D71 |
| hypocenter | C71 | #2971 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C8×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×C71⋊C8 | C2 | semidirect |
| 3. #17986078 | C2 | semidirect |
| 4. #17986076 | C2 | semidirect |
| 5. #17986055 | C2 | semidirect |
| 6. C4×#11765848 | C2 | semidirect |
| 7. C8×Q8×C71 | C2 | semidirect |
| 44. Q8×C71 | M16 | semidirect |
| 57. C8×C71 | #41 | semidirect |
| 59. C71⋊C8 | #41 | semidirect |
| 76. C71 | #2971 | semidirect |
| 79. C8×Q8 | D71 | semidirect |
| 120. Q8 | #11765848 | semidirect |
| 135. C8 | #11765866 | semidirect |