Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #5240 | C2 | semidirect |
| 3. #5237 | C2 | semidirect |
| 4. #4536 | C2 | semidirect |
| 7. C22×C3×D4 | C4 | semidirect |
| 12. C3×#120 | C4 | semidirect |
| 14. C3×#117 | C4 | semidirect |
| 53. C22×D4 | Dic3 | semidirect |
| 59. #120 | Dic3 | semidirect |
| 62. #117 | Dic3 | semidirect |
| 192. C3 | #2122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5240 | 2 |
| #5237 | 2 |
| #4536 | 2 |
| #2122 | 3 |