Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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. D3×#101 | C2 | semidirect |
| 3. C3×#355 | C2 | semidirect |
| 4. #4542 | C2 | semidirect |
| 5. #4477 | C2 | semidirect |
| 17. C3×#101 | C22 | semidirect |
| 18. #836 | C22 | semidirect |
| 24. #355 | D3 | direct (N × H) |
| 62. #101 | C2×D3 | semidirect |
| 159. D3 | #355 | direct (N × H) |
| 176. C3 | C2×#355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#124 | 2 |
| D3×#101 | 2 |
| C3×#355 | 2 |
| #4542 | 2 |
| #4477 | 2 |
| C2×#355 | 3 |