Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
254 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 63 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×#824 | C2 | semidirect |
| 4. #5124 | C2 | semidirect |
| 6. #5004 | C2 | semidirect |
| 7. C3×#344 | C2 | semidirect |
| 32. #344 | D3 | semidirect |
| 205. C3 | #2049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| C2×#824 | 2 |
| #5132 | 2 |
| #5124 | 2 |
| #5005 | 2 |
| #5004 | 2 |
| C3×#344 | 2 |
| #2049 | 3 |