Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5827 | C2 | semidirect |
| 3. C3×#408 | C2 | semidirect |
| 4. #5133 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 6. #5113 | C2 | semidirect |
| 7. C2×#818 | C2 | semidirect |
| 8. #4737 | C2 | semidirect |
| 9. #4736 | C2 | semidirect |
| 10. #4723 | C2 | semidirect |
| 11. #4722 | C2 | semidirect |
| 52. #408 | D3 | semidirect |
| 260. C3 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5833 | 2 |
| #5827 | 2 |
| C3×#408 | 2 |
| #5133 | 2 |
| #5121 | 2 |
| #5113 | 2 |
| C2×#818 | 2 |
| #4737 | 2 |
| #4736 | 2 |
| #4723 | 2 |
| #4722 | 2 |
| #3098 | 3 |