Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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. C3×#536 | C2 | semidirect |
| 2. C2×#951 | C2 | semidirect |
| 4. C22×#216 | C2 | semidirect |
| 5. C2×#942 | C2 | semidirect |
| 6. #5526 | C2 | semidirect |
| 7. #5092 | C2 | semidirect |
| 8. #5086 | C2 | semidirect |
| 9. #5060 | C2 | semidirect |
| 10. #5059 | C2 | semidirect |
| 11. #4997 | C2 | semidirect |
| 49. #536 | D3 | semidirect |
| 281. C3 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#536 | 2 |
| C2×#951 | 2 |
| C2×#950 | 2 |
| C22×#216 | 2 |
| C2×#942 | 2 |
| #5526 | 2 |
| #5092 | 2 |
| #5086 | 2 |
| #5060 | 2 |
| #5059 | 2 |
| #4997 | 2 |
| #3156 | 3 |