Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
522 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 155 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×C3×C4⋊C16 | C2 | semidirect |
| 3. C2×(C2×D3)⋊C16 | C2 | semidirect |
| 4. C2×#4461 | C2 | semidirect |
| 19. C2×C4⋊C16 | D3 | semidirect |
| 43. C2×C3⋊C16 | D4 | semidirect |
| 221. C3 | #13190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D12 | 2 |
| C2×C3×C4⋊C16 | 2 |
| C2×(C2×D3)⋊C16 | 2 |
| C2×#4461 | 2 |
| #13190 | 3 |