Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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. #5603 | C2 | semidirect |
| 3. #5153 | C2 | semidirect |
| 4. #5116 | C2 | semidirect |
| 5. #5102 | C2 | semidirect |
| 6. #5042 | C2 | semidirect |
| 7. #4875 | C2 | semidirect |
| 8. #4767 | C2 | semidirect |
| 9. #4759 | C2 | semidirect |
| 205. C3 | #3262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5603 | 2 |
| C3×#466 | 2 |
| #5153 | 2 |
| #5116 | 2 |
| #5102 | 2 |
| #5042 | 2 |
| #4875 | 2 |
| #4767 | 2 |
| #4759 | 2 |
| #3262 | 3 |