Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C3×C4⋊Q8 | C2 | semidirect |
| 3. #5088 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5078 | C2 | semidirect |
| 6. #4967 | C2 | semidirect |
| 7. #4925 | C2 | semidirect |
| 31. C2×C4⋊Q8 | D3 | semidirect |
| 193. C3 | #3226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊Q8 | 2 |
| #5477 | 2 |
| #5088 | 2 |
| #5087 | 2 |
| #5078 | 2 |
| #4967 | 2 |
| #4925 | 2 |
| #3226 | 3 |