Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #16863746 | C2 | semidirect |
| 3. #16863724 | C2 | semidirect |
| 4. #16863681 | C2 | semidirect |
| 5. #16863627 | C2 | semidirect |
| 6. #16863598 | C2 | semidirect |
| 7. #16863535 | C2 | semidirect |
| 8. C4×#11761615 | C2 | semidirect |
| 9. D4×C67⋊C8 | C2 | semidirect |
| 10. C2×#14523967 | C2 | semidirect |
| 11. D4×Q8×C67 | C2 | semidirect |
| 83. Q8×C67 | #41 | semidirect |
| 84. D4×C67 | SD16 | semidirect |
| 129. C67 | #3298 | semidirect |
| 130. D4×Q8 | D67 | semidirect |
| 213. Q8 | #11761627 | semidirect |
| 217. D4 | #11761615 | semidirect |