Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5518 | C2 | semidirect |
| 3. #5075 | C2 | semidirect |
| 4. #5063 | C2 | semidirect |
| 5. #5042 | C2 | semidirect |
| 6. #5041 | C2 | semidirect |
| 7. #5019 | C2 | semidirect |
| 8. #5009 | C2 | semidirect |
| 9. #4999 | C2 | semidirect |
| 196. C3 | #3260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#540 | 2 |
| #5518 | 2 |
| #5075 | 2 |
| #5063 | 2 |
| #5042 | 2 |
| #5041 | 2 |
| #5019 | 2 |
| #5009 | 2 |
| #4999 | 2 |
| #3260 | 3 |