Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
312 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 109 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⋊C8 | C2 | semidirect |
| 4. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. #4550 | C2 | semidirect |
| 23. C2×C4⋊C8 | D3 | semidirect |
| 196. C3 | #1798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#872 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4550 | 2 |
| #1798 | 3 |