Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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. C3×#418 | C2 | semidirect |
| 3. C2×#833 | C2 | semidirect |
| 4. C2×#823 | C2 | semidirect |
| 5. C2×#822 | C2 | semidirect |
| 6. #5001 | C2 | semidirect |
| 7. #4997 | C2 | semidirect |
| 16. C2×#213 | C4 | semidirect |
| 30. #418 | D3 | semidirect |
| 216. C3 | #1978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#213 | 2 |
| C3×#418 | 2 |
| C2×#833 | 2 |
| C2×#823 | 2 |
| C2×#822 | 2 |
| #5001 | 2 |
| #4997 | 2 |
| #1978 | 3 |