Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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. C3×C4×C4⋊C4 | C2 | semidirect |
| 4. Dic3×C4⋊C4 | C2 | semidirect |
| 5. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #4932 | C2 | semidirect |
| 7. #4666 | C2 | semidirect |
| 8. D3×#95 | C2 | semidirect |
| 21. #893 | C4 | semidirect |
| 22. C4×D12 | C4 | semidirect |
| 31. C4×C4⋊C4 | D3 | semidirect |
| 49. C2×C4×D3 | C2×C4 | semidirect |
| 50. C2×C4×D3 | C2×C4 | semidirect |
| 51. C3×C4⋊C4 | C2×C4 | semidirect |
| 53. C3×C42 | C2×C4 | semidirect |
| 54. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 55. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 56. C4⋊Dic3 | C2×C4 | semidirect |
| 58. C4×Dic3 | C2×C4 | semidirect |
| 101. D12 | C42 | semidirect |
| 120. C4⋊C4 | C4×D3 | semidirect |
| 126. C42 | C4×D3 | semidirect |
| 194. C3 | #2275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#893 | 2 |
| C2×C4×D12 | 2 |
| C3×C4×C4⋊C4 | 2 |
| Dic3×C4⋊C4 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4932 | 2 |
| #4666 | 2 |
| D3×#95 | 2 |
| #2275 | 3 |