Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic134 | C2 | semidirect |
| 2. C2×#14524073 | C2 | semidirect |
| 3. #16863551 | C2 | semidirect |
| 4. #16863534 | C2 | semidirect |
| 5. #16863404 | C2 | semidirect |
| 6. #16863360 | C2 | semidirect |
| 15. C2×#11761618 | C22 | semidirect |
| 16. C2×#11761616 | C22 | semidirect |
| 18. #14523966 | C22 | semidirect |
| 34. C2×Dic134 | D4 | semidirect |
| 95. C22×C67 | #137 | semidirect |
| 109. C67 | #3004 | semidirect |
| 204. C22 | #14524073 | semidirect |