Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
584 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#11761615 | C2 | semidirect |
| 3. #16863596 | C2 | direct (N × H) |
| 4. C2×C4⋊(C67⋊C8) | C2 | semidirect |
| 5. C2×#14523963 | C2 | semidirect |
| 6. C2×C4×Q8×C67 | C2 | semidirect |
| 11. C2×#11761615 | C22 | semidirect |
| 15. C4⋊(C67⋊C8) | C22 | semidirect |
| 16. #14523963 | C22 | semidirect |
| 19. C4×Q8×C67 | C22 | semidirect |
| 38. C2×Q8×C67 | D4 | semidirect |
| 58. Q8×C67 | C2×D4 | semidirect |
| 64. C2×C4×C67 | SD16 | semidirect |
| 89. C4×C67 | C2×SD16 | semidirect |
| 92. C2×C67 | #460 | semidirect |
| 98. C67 | C2×#460 | semidirect |
| 101. C2×C4×Q8 | D67 | semidirect |
| 115. C4×Q8 | C2×D67 | semidirect |
| 125. C2×Q8 | D268 | semidirect |
| 156. Q8 | C2×D268 | semidirect |
| 167. C2×C4 | #11761615 | semidirect |
| 187. C4 | C2×#11761615 | semidirect |
| 191. C2 | #16863596 | direct (N × H) |