Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C3×#536 | C2 | semidirect |
| 3. C22×#216 | C2 | semidirect |
| 4. C2×#942 | C2 | semidirect |
| 5. #5234 | C2 | semidirect |
| 6. #5050 | C2 | semidirect |
| 7. #5047 | C2 | semidirect |
| 8. #5004 | C2 | semidirect |
| 9. #5002 | C2 | semidirect |
| 41. #536 | D3 | semidirect |
| 275. C3 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010 | 2 |
| C3×#536 | 2 |
| C22×#216 | 2 |
| C2×#942 | 2 |
| #5234 | 2 |
| #5050 | 2 |
| #5047 | 2 |
| #5004 | 2 |
| #5002 | 2 |
| #3011 | 3 |