Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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×D3×C16 | C2 | semidirect |
| 3. C3×C4⋊C16 | C2 | semidirect |
| 4. (C2×D3)⋊C16 | C2 | semidirect |
| 5. C4×C3⋊C16 | C2 | semidirect |
| 18. C4⋊C16 | D3 | semidirect |
| 33. C3⋊C16 | D4 | semidirect |
| 48. D12 | C16 | semidirect |
| 71. C2×D3 | C2×C16 | semidirect |
| 73. C3×C4 | C2×C16 | semidirect |
| 99. C4 | D3×C16 | semidirect |
| 102. C3 | D4×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C16 | 2 |
| C8×D12 | 2 |
| C3×C4⋊C16 | 2 |
| (C2×D3)⋊C16 | 2 |
| C4×C3⋊C16 | 2 |
| D4×C16 | 3 |