Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #5470 | C2 | semidirect |
| 3. C3×#423 | C2 | semidirect |
| 4. #5134 | C2 | semidirect |
| 5. #4850 | C2 | semidirect |
| 6. #4848 | C2 | semidirect |
| 7. #4846 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 41. #423 | D3 | semidirect |
| 219. C3 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| #5470 | 2 |
| C3×#423 | 2 |
| #5134 | 2 |
| #4850 | 2 |
| #4848 | 2 |
| #4846 | 2 |
| #4841 | 2 |
| #3254 | 3 |