Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#822 | C2 | semidirect |
| 5. C2×#810 | C2 | semidirect |
| 7. C3×#343 | C2 | semidirect |
| 32. #343 | D3 | semidirect |
| 212. C3 | #2052 | 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 |
| #5129 | 2 |
| C2×#822 | 2 |
| C2×#810 | 2 |
| #4966 | 2 |
| C3×#343 | 2 |
| #2052 | 3 |