Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
736 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C2×C3×#101 | C2 | semidirect |
| 4. C2×#836 | C2 | semidirect |
| 5. C2×#824 | C2 | semidirect |
| 6. D3×#101 | C2 | direct (N × H) |
| 24. C3×#101 | C22 | semidirect |
| 25. #836 | C22 | semidirect |
| 26. #824 | C22 | semidirect |
| 32. C2×#101 | D3 | direct (N × H) |
| 88. #101 | C2×D3 | direct (N × H) |
| 165. C2×D3 | #101 | direct (N × H) |
| 207. C2×C3 | C2×#101 | semidirect |
| 210. D3 | C2×#101 | direct (N × H) |
| 226. C3 | C22×#101 | semidirect |
| 231. C2 | D3×#101 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×Q8 | 2 |
| C2×D3×M16 | 2 |
| C2×C3×#101 | 2 |
| C2×#836 | 2 |
| C2×#824 | 2 |
| D3×#101 | 2 |
| C22×#101 | 3 |