Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
726 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 253 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×#131 | C2 | semidirect |
| 3. #5827 | C2 | semidirect |
| 4. #5133 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. #5113 | C2 | semidirect |
| 7. C2×#816 | C2 | semidirect |
| 11. #1010 | C4 | semidirect |
| 29. C2×#131 | D3 | semidirect |
| 46. #235 | C2×C4 | semidirect |
| 51. C2×Dic6 | C2×C4 | semidirect |
| 183. C3 | #2898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010 | 2 |
| C2×C3×#131 | 2 |
| #5827 | 2 |
| #5133 | 2 |
| #5120 | 2 |
| #5113 | 2 |
| C2×#816 | 2 |
| #2898 | 3 |