Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#14524032 | C2 | semidirect |
| 3. C2×#14523970 | C2 | semidirect |
| 4. #16863405 | C2 | semidirect |
| 5. C2×#14523959 | C2 | semidirect |
| 6. #16863157 | C2 | semidirect |
| 7. C2×#137×C67 | C2 | semidirect |
| 47. C4×Dic67 | D4 | semidirect |
| 58. C2×Q8×C67 | D4 | semidirect |
| 67. M16×C67 | D4 | semidirect |
| 132. C67 | #2004 | semidirect |
| 133. C2×#137 | D67 | semidirect |
| 172. C2×Q8 | C22⋊D67 | semidirect |
| 191. M16 | C22⋊D67 | semidirect |