Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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×#533 | C2 | semidirect |
| 3. #5091 | C2 | semidirect |
| 4. #5090 | C2 | semidirect |
| 5. #5084 | C2 | semidirect |
| 6. #5083 | C2 | semidirect |
| 7. #5052 | C2 | semidirect |
| 9. #5028 | C2 | semidirect |
| 10. #5022 | C2 | semidirect |
| 11. #4924 | C2 | semidirect |
| 44. #533 | D3 | semidirect |
| 261. C3 | #3252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| #5479 | 2 |
| #5091 | 2 |
| #5090 | 2 |
| #5084 | 2 |
| #5083 | 2 |
| #5052 | 2 |
| #5049 | 2 |
| #5028 | 2 |
| #5022 | 2 |
| #4924 | 2 |
| #3252 | 3 |