Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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×#798 | C2 | semidirect |
| 3. C3×C22⋊C16 | C2 | semidirect |
| 4. #4549 | C2 | semidirect |
| 5. (C2×D3)⋊C16 | C2 | semidirect |
| 15. C2×C3×C16 | C22 | semidirect |
| 16. C2×C3⋊C16 | C22 | semidirect |
| 22. C22⋊C16 | D3 | semidirect |
| 54. C2×C16 | C2×D3 | semidirect |
| 101. C22×C3 | M32 | semidirect |
| 109. C2×D3 | M32 | semidirect |
| 153. C22 | #798 | semidirect |
| 160. C3 | #2112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×#798 | 2 |
| C3×C22⋊C16 | 2 |
| #4549 | 2 |
| (C2×D3)⋊C16 | 2 |
| #2112 | 3 |