Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#14524076 | C2 | semidirect |
| 3. C2×#14524030 | C2 | semidirect |
| 4. C2×#14523969 | C2 | semidirect |
| 5. #16863406 | C2 | semidirect |
| 6. #16863157 | C2 | semidirect |
| 7. C2×#100×C67 | C2 | semidirect |
| 39. C2×Dic134 | D4 | semidirect |
| 54. C4×Dic67 | D4 | semidirect |
| 66. M16×C67 | D4 | semidirect |
| 132. C67 | #2004 | semidirect |
| 138. C2×#100 | D67 | semidirect |
| 191. M16 | C22⋊D67 | semidirect |