Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #459×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #459 | D71 |
| hypocenter | C71 | #3284 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556147 | C2 | semidirect |
| 2. #17986669 | C2 | semidirect |
| 3. #17986653 | C2 | semidirect |
| 4. #17986371 | C2 | semidirect |
| 5. #17986227 | C2 | semidirect |
| 6. #17986210 | C2 | semidirect |
| 7. #17986162 | C2 | semidirect |
| 8. #17986141 | C2 | semidirect |
| 9. C4×#11765853 | C2 | semidirect |
| 10. #17986064 | C2 | semidirect |
| 11. #459×C71 | C2 | semidirect |
| 58. #11765853 | D4 | semidirect |
| 127. C4×C71 | #135 | semidirect |
| 141. C71 | #3284 | semidirect |
| 148. #459 | D71 | semidirect |
| 272. C4 | #14556147 | semidirect |