Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5570 | C2 | semidirect |
| 3. C3×#475 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 7. #4856 | C2 | semidirect |
| 9. #4831 | C2 | semidirect |
| 11. #4793 | C2 | semidirect |
| 48. #475 | D3 | semidirect |
| 69. #215 | Q8 | semidirect |
| 117. C3×Q8 | C2×Q8 | semidirect |
| 137. C3⋊C8 | C2×Q8 | semidirect |
| 191. Q8 | D3×Q8 | semidirect |
| 228. C3 | #3386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5727 | 2 |
| #5570 | 2 |
| C3×#475 | 2 |
| #5078 | 2 |
| C4×#215 | 2 |
| #4871 | 2 |
| #4856 | 2 |
| #4846 | 2 |
| #4831 | 2 |
| #4817 | 2 |
| #4793 | 2 |
| #3386 | 3 |