Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
494 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#14524063 | C2 | semidirect |
| 2. #16864067 | C2 | semidirect |
| 3. #16863770 | C2 | semidirect |
| 4. #16863627 | C2 | semidirect |
| 5. #16863603 | C2 | semidirect |
| 6. #16863591 | C2 | semidirect |
| 7. #16863556 | C2 | semidirect |
| 8. #16863541 | C2 | semidirect |
| 9. C4×#11761616 | C2 | semidirect |
| 10. D4×C67⋊C8 | C2 | semidirect |
| 11. #547×C67 | C2 | semidirect |
| 52. #11761616 | D4 | semidirect |
| 129. C4×C67 | #135 | semidirect |
| 141. C67 | #3284 | semidirect |
| 144. #547 | D67 | semidirect |
| 272. C4 | #14524063 | semidirect |