Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #5094 | C2 | semidirect |
| 4. #5093 | C2 | semidirect |
| 5. #5052 | C2 | semidirect |
| 6. #5050 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. C4×#216 | C2 | semidirect |
| 10. #5004 | C2 | semidirect |
| 11. #4996 | C2 | semidirect |
| 238. C3 | #3328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#556 | 2 |
| D4×Dic6 | 2 |
| #5094 | 2 |
| #5093 | 2 |
| #5052 | 2 |
| #5050 | 2 |
| #5031 | 2 |
| C4×#216 | 2 |
| #5012 | 2 |
| #5004 | 2 |
| #4996 | 2 |
| #3328 | 3 |