Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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×Q82 | C2 | semidirect |
| 3. #5094 | C2 | semidirect |
| 4. #5093 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. #5030 | C2 | semidirect |
| 11. #5024 | C2 | semidirect |
| 42. Q82 | D3 | semidirect |
| 228. C3 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q82 | 2 |
| #5584 | 2 |
| #5094 | 2 |
| #5093 | 2 |
| #5089 | 2 |
| #5084 | 2 |
| #5031 | 2 |
| #5030 | 2 |
| #5028 | 2 |
| C4×#215 | 2 |
| #5024 | 2 |
| #3369 | 3 |