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. #5234 | C2 | semidirect |
| 4. #5233 | C2 | semidirect |
| 5. #5232 | C2 | semidirect |
| 6. #5045 | C2 | semidirect |
| 7. #5044 | C2 | semidirect |
| 8. #5035 | C2 | semidirect |
| 9. #5033 | C2 | semidirect |
| 10. #4964 | C2 | semidirect |
| 11. C2×#807 | C2 | semidirect |
| 260. C3 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#537 | 2 |
| #5827 | 2 |
| #5234 | 2 |
| #5233 | 2 |
| #5232 | 2 |
| #5045 | 2 |
| #5044 | 2 |
| #5035 | 2 |
| #5033 | 2 |
| #4964 | 2 |
| C2×#807 | 2 |
| #3098 | 3 |