Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
260 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 69 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×C3×#101 | C2 | semidirect |
| 3. C2×#836 | C2 | semidirect |
| 4. #4477 | C2 | direct (N × H) |
| 18. C3×#101 | C22 | semidirect |
| 20. #836 | C22 | semidirect |
| 23. C2×#101 | D3 | semidirect |
| 66. #101 | C2×D3 | semidirect |
| 165. C2×C3 | #355 | semidirect |
| 183. C3 | C2×#355 | semidirect |
| 187. C2 | #4477 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#947 | 2 |
| C2×C3×#101 | 2 |
| C2×#836 | 2 |
| #4477 | 2 |
| C2×#355 | 3 |