Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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×#106 | C2 | semidirect |
| 5. C2×#808 | C2 | semidirect |
| 6. #4551 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 23. (C2×D3)⋊C8 | C4 | semidirect |
| 27. C2×#106 | D3 | semidirect |
| 50. C2×C3×C8 | C2×C4 | semidirect |
| 63. C2×C3⋊C8 | C2×C4 | semidirect |
| 137. C2×C8 | C4×D3 | semidirect |
| 161. C2×D3 | #106 | semidirect |
| 238. C3 | #1853 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C4⋊C4 | 2 |
| C2×C3×#106 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| #4987 | 2 |
| C2×#808 | 2 |
| #4551 | 2 |
| #4529 | 2 |
| #1853 | 3 |