Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5579 | C2 | semidirect |
| 3. #5087 | C2 | semidirect |
| 4. #5084 | C2 | semidirect |
| 5. #5081 | C2 | semidirect |
| 6. #5080 | C2 | semidirect |
| 7. #5024 | C2 | semidirect |
| 10. #5009 | C2 | semidirect |
| 11. #5008 | C2 | semidirect |
| 43. D4×Q8 | D3 | semidirect |
| 74. #213 | Q8 | semidirect |
| 133. D12 | C2×Q8 | semidirect |
| 139. C3⋊C8 | C2×Q8 | semidirect |
| 237. C3 | #3384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Q8 | 2 |
| #5579 | 2 |
| #5087 | 2 |
| #5084 | 2 |
| #5081 | 2 |
| #5080 | 2 |
| #5024 | 2 |
| #5014 | 2 |
| C4×#213 | 2 |
| #5009 | 2 |
| #5008 | 2 |
| #3384 | 3 |