Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 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×#97 | C2 | semidirect |
| 3. C2×#803 | C2 | semidirect |
| 4. #4464 | C2 | direct (N × H) |
| 18. C3×#97 | C22 | semidirect |
| 20. #803 | C22 | semidirect |
| 23. C2×#97 | D3 | semidirect |
| 62. #97 | C2×D3 | semidirect |
| 145. C2×C3 | #329 | semidirect |
| 165. C3 | C2×#329 | semidirect |
| 167. C2 | #4464 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| C2×C3×#97 | 2 |
| C2×#803 | 2 |
| #4464 | 2 |
| C2×#329 | 3 |