Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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×#520 | C2 | semidirect |
| 3. #5234 | C2 | semidirect |
| 4. #5003 | C2 | semidirect |
| 5. #5002 | C2 | semidirect |
| 6. #4996 | C2 | semidirect |
| 7. #4995 | C2 | semidirect |
| 8. #4970 | C2 | semidirect |
| 9. #4967 | C2 | semidirect |
| 10. #4966 | C2 | semidirect |
| 11. C2×#807 | C2 | semidirect |
| 43. #520 | D3 | semidirect |
| 260. C3 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#520 | 2 |
| #5833 | 2 |
| #5234 | 2 |
| #5003 | 2 |
| #5002 | 2 |
| #4996 | 2 |
| #4995 | 2 |
| #4970 | 2 |
| #4967 | 2 |
| #4966 | 2 |
| C2×#807 | 2 |
| #3098 | 3 |