Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. C2×Dic3⋊C8 | C2 | semidirect |
| 5. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 6. C3×#336 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 32. #336 | D3 | semidirect |
| 55. (C2×D3)⋊C4 | C8 | semidirect |
| 95. C2×C3×C4 | C2×C8 | semidirect |
| 110. C2×Dic3 | C2×C8 | semidirect |
| 164. C2×D3 | C4⋊C8 | semidirect |
| 200. C2×C4 | D3×C8 | semidirect |
| 242. C3 | #1850 | 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×(C2×D3)⋊C8 | 2 |
| C2×Dic3⋊C8 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C3×#336 | 2 |
| #4550 | 2 |
| #1850 | 3 |