Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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×#944 | C2 | semidirect |
| 5. C3×#419 | C2 | semidirect |
| 6. #5118 | C2 | semidirect |
| 7. #5004 | C2 | semidirect |
| 8. #4818 | C2 | semidirect |
| 9. #4795 | C2 | semidirect |
| 44. #419 | D3 | semidirect |
| 189. Dic3 | #137 | semidirect |
| 238. C3 | #3039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#944 | 2 |
| C2×#942 | 2 |
| C2×#909 | 2 |
| #5522 | 2 |
| C3×#419 | 2 |
| #5118 | 2 |
| #5004 | 2 |
| #4818 | 2 |
| #4795 | 2 |
| #3039 | 3 |