Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 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×#798 | C2 | semidirect |
| 3. C3×C4×C16 | C2 | semidirect |
| 4. (C2×D3)⋊C16 | C2 | semidirect |
| 5. C4⋊(C3⋊C16) | C2 | semidirect |
| 20. C4×C16 | D3 | semidirect |
| 32. C3×C16 | D4 | semidirect |
| 67. C16 | D12 | semidirect |
| 73. C3×C4 | M32 | semidirect |
| 99. C4 | #798 | semidirect |
| 102. C3 | #2169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#798 | 2 |
| C8×D12 | 2 |
| C3×C4×C16 | 2 |
| (C2×D3)⋊C16 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2169 | 3 |