Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 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. C2×#14524068 | C2 | semidirect |
| 2. C2×#14524040 | C2 | semidirect |
| 3. #16863596 | C2 | semidirect |
| 4. #16863591 | C2 | semidirect |
| 5. #16863420 | C2 | semidirect |
| 6. #16863400 | C2 | semidirect |
| 7. C4×#41×C67 | C2 | semidirect |
| 11. C2×#11761615 | C22 | semidirect |
| 12. C2×#11761613 | C22 | semidirect |
| 17. C4⋊(C67⋊C8) | C22 | semidirect |
| 18. #14523963 | C22 | semidirect |
| 20. C4×Q8×C67 | C22 | semidirect |
| 22. C4×D4×C67 | C22 | semidirect |
| 40. #41×C67 | D4 | semidirect |
| 63. Q8×C67 | C2×D4 | semidirect |
| 66. D4×C67 | C2×D4 | semidirect |
| 96. C4×C67 | AGL(1,ℤ/8) | semidirect |
| 105. C67 | #3038 | semidirect |
| 108. C4×#41 | D67 | semidirect |
| 123. C4×Q8 | C2×D67 | semidirect |
| 125. C4×D4 | C2×D67 | semidirect |
| 134. #41 | D268 | semidirect |
| 168. Q8 | C2×D268 | semidirect |
| 176. D4 | C2×D268 | semidirect |
| 201. C4 | #14524068 | semidirect |