Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 424 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. #5093 | C2 | semidirect |
| 4. #5089 | C2 | semidirect |
| 5. #5088 | C2 | semidirect |
| 6. #4966 | C2 | semidirect |
| 7. C4×#208 | C2 | semidirect |
| 31. C2×C4⋊Q8 | D3 | semidirect |
| 195. C3 | #3141 | 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 |
| #5093 | 2 |
| #5089 | 2 |
| #5088 | 2 |
| #4966 | 2 |
| C4×#208 | 2 |
| #3141 | 3 |