Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14523984 | C2 | semidirect |
| 2. #16863773 | C2 | semidirect |
| 3. C4⋊(C67⋊C16) | C2 | semidirect |
| 4. #16863196 | C2 | semidirect |
| 5. C4×D8×C67 | C2 | semidirect |
| 26. D8×C67 | D4 | semidirect |
| 57. C4×C67 | D16 | semidirect |
| 66. C67 | #2206 | semidirect |
| 69. C4×D8 | D67 | semidirect |
| 91. D8 | D268 | semidirect |
| 123. C4 | #14523984 | semidirect |