Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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. #16863474 | C2 | semidirect |
| 3. #16863473 | C2 | semidirect |
| 4. #16863146 | C2 | semidirect |
| 5. #16863125 | C2 | semidirect |
| 6. #16863118 | C2 | semidirect |
| 7. D4⋊C8×C67 | C2 | semidirect |
| 63. C67⋊C8 | M16 | semidirect |
| 84. C67 | #1594 | semidirect |
| 90. D4⋊C8 | D67 | semidirect |