Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. #5833 | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. C2×#908 | C2 | semidirect |
| 4. C2×C3×#104 | C2 | semidirect |
| 5. #4939 | C2 | semidirect |
| 6. C2×#805 | C2 | semidirect |
| 7. #4554 | C2 | semidirect |
| 36. C2×#104 | D3 | semidirect |
| 63. C2×D12 | D4 | semidirect |
| 67. C3×M16 | D4 | semidirect |
| 80. #208 | D4 | semidirect |
| 185. M16 | #67 | semidirect |
| 296. C3 | #2006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5833 | 2 |
| C2×#949 | 2 |
| C2×#908 | 2 |
| C2×C3×#104 | 2 |
| #4939 | 2 |
| C2×#805 | 2 |
| #4554 | 2 |
| #2006 | 3 |