Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 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 | C24×D71 |
| commutator, socle | C22×C71 | C25 |
| Fitting | #519×C71 | C2 |
| hypercenter | #519 | D71 |
| hypocenter | C71 | #3486 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556176 | C2 | semidirect |
| 2. C22×Q8×D71 | C2 | semidirect |
| 3. Q8×D284 | C2 | semidirect |
| 4. #17986661 | C2 | semidirect |
| 5. #17986575 | C2 | semidirect |
| 6. #17986511 | C2 | semidirect |
| 7. #519×C71 | C2 | semidirect |
| 9. C2×#11765866 | C22 | semidirect |
| 14. C2×Q8×D71 | C22 | semidirect |
| 16. #14556128 | C22 | semidirect |
| 17. #14556116 | C22 | semidirect |
| 20. #14556108 | C22 | semidirect |
| 25. C4×Q8×C71 | C22 | semidirect |
| 45. C2×Q8×C71 | D4 | semidirect |
| 78. C2×D71 | 2−1+4 | semidirect |
| 89. C71 | #3486 | semidirect |
| 96. #519 | D71 | semidirect |
| 113. C4×Q8 | C2×D71 | semidirect |
| 124. C2×Q8 | D284 | semidirect |