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 |
|---|---|---|
| 2. #5470 | C2 | semidirect |
| 3. #5063 | C2 | semidirect |
| 4. #5054 | C2 | semidirect |
| 5. #5052 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. #5021 | C2 | semidirect |
| 9. #5019 | C2 | semidirect |
| 10. #5008 | C2 | semidirect |
| 11. #4924 | C2 | 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×#529 | 2 |
| #5470 | 2 |
| #5063 | 2 |
| #5054 | 2 |
| #5052 | 2 |
| #5042 | 2 |
| #5031 | 2 |
| #5021 | 2 |
| #5019 | 2 |
| #5008 | 2 |
| #4924 | 2 |
| #3252 | 3 |