Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C3×D4×Q8 | C2 | semidirect |
| 2. Q8×D12 | C2 | semidirect |
| 3. #5087 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 5. Q8×C3⋊C8 | C2 | semidirect |
| 7. #5007 | C2 | semidirect |
| 26. D4×Q8 | D3 | semidirect |
| 46. #213 | Q8 | direct (N × H) |
| 71. C3×Q8 | D8 | semidirect |
| 73. C3×D4 | C2×Q8 | semidirect |
| 81. D12 | C2×Q8 | semidirect |
| 85. C3⋊C8 | C2×Q8 | semidirect |
| 123. Q8 | #213 | direct (N × H) |
| 127. D4 | D3×Q8 | semidirect |
| 155. C3 | Q8×D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Q8 | 2 |
| Q8×D12 | 2 |
| #5087 | 2 |
| #5078 | 2 |
| Q8×C3⋊C8 | 2 |
| C4×#213 | 2 |
| #5007 | 2 |
| Q8×D8 | 3 |