Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
192 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 73 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×C8×D4 | C2 | semidirect |
| 3. C8×D12 | C2 | semidirect |
| 4. D4⋊(C3⋊C8) | C2 | semidirect |
| 5. #4483 | C2 | semidirect |
| 6. #4480 | C2 | semidirect |
| 7. #4454 | C2 | semidirect |
| 26. C8×D4 | D3 | semidirect |
| 42. #213 | C8 | semidirect |
| 68. C3×D4 | C2×C8 | semidirect |
| 77. D12 | C2×C8 | semidirect |
| 86. C3⋊C8 | C2×C8 | semidirect |
| 125. D4 | D3×C8 | semidirect |
| 161. C3 | #1580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×D4 | 2 |
| C4×#213 | 2 |
| C8×D12 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4483 | 2 |
| #4480 | 2 |
| #4454 | 2 |
| #1580 | 3 |