Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1088 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 285 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×#117 | C2 | semidirect |
| 3. C2×#926 | C2 | semidirect |
| 4. #4987 | C2 | semidirect |
| 6. #4943 | C2 | semidirect |
| 7. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 14. C22×C4×D3 | C4 | semidirect |
| 18. C2×C3×C4⋊C4 | C22 | semidirect |
| 20. C2×C3×C42 | C22 | semidirect |
| 24. C2×C4⋊Dic3 | C22 | semidirect |
| 25. C2×C4×Dic3 | C22 | semidirect |
| 26. C3⋊#95 | C22 | semidirect |
| 29. C2×#117 | D3 | semidirect |
| 76. C2×C4⋊C4 | C2×D3 | semidirect |
| 81. C2×C42 | C2×D3 | semidirect |
| 99. C2×C3×C4 | C22⋊C4 | semidirect |
| 158. C2×D3 | #117 | semidirect |
| 188. C2×C4 | (C2×D3)⋊C4 | semidirect |
| 220. C3 | #2280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D3 | 2 |
| C2×C3×#117 | 2 |
| C2×#926 | 2 |
| #4987 | 2 |
| #4955 | 2 |
| #4943 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #2280 | 3 |