Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 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. C3×C4×C4⋊C4 | C2 | semidirect |
| 4. C2×C4×C3⋊C8 | C2 | semidirect |
| 5. #4529 | C2 | semidirect |
| 16. C4×D12 | C4 | semidirect |
| 18. #809 | C4 | direct (N × H) |
| 23. C4×C4⋊C4 | D3 | semidirect |
| 39. C3×C4⋊C4 | C2×C4 | semidirect |
| 48. C2×C3⋊C8 | C2×C4 | semidirect |
| 85. D12 | C42 | semidirect |
| 107. C4⋊C4 | C4×D3 | semidirect |
| 124. C3×C4 | #102 | semidirect |
| 174. C4 | #809 | direct (N × H) |
| 178. C3 | C4×#102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D12 | 2 |
| C3×C4×C4⋊C4 | 2 |
| C2×#809 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #4529 | 2 |
| C4×#102 | 3 |