Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #16863870 | C2 | semidirect |
| 3. #16863414 | C2 | semidirect |
| 4. #16863412 | C2 | semidirect |
| 5. C2×#14523959 | C2 | semidirect |
| 6. #16863152 | C2 | semidirect |
| 7. H(3,ℤ/4)×C67 | C2 | semidirect |
| 11. #14524040 | C4 | semidirect |
| 12. #14524031 | C4 | semidirect |
| 30. C2×Dic134 | C2×C4 | semidirect |
| 37. C2×D268 | C2×C4 | semidirect |
| 49. C4×Dic67 | D4 | semidirect |
| 58. C42×C67 | C2×C4 | semidirect |
| 59. C42×C67 | D4 | semidirect |
| 117. C67 | #1911 | semidirect |
| 124. H(3,ℤ/4) | D67 | semidirect |
| 175. C42 | C4×D67 | semidirect |
| 176. C42 | D268 | semidirect |