Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 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. C2×C3×C4⋊Q8 | C2 | semidirect |
| 4. #5225 | C2 | semidirect |
| 5. #5090 | C2 | semidirect |
| 6. #5083 | C2 | semidirect |
| 7. #4924 | C2 | semidirect |
| 29. C2×C4⋊Q8 | D3 | semidirect |
| 144. C3×C4 | #137 | semidirect |
| 187. C4 | #942 | semidirect |
| 190. C3 | #3039 | 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 |
| C2×#942 | 2 |
| C4×#235 | 2 |
| #5225 | 2 |
| #5090 | 2 |
| #5083 | 2 |
| #4924 | 2 |
| #3039 | 3 |