Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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. #5819 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. #5215 | C2 | semidirect |
| 5. #4531 | C2 | semidirect |
| 9. C3×#127 | C4 | semidirect |
| 10. C3×#124 | C4 | semidirect |
| 49. C2×C3⋊C8 | D4 | semidirect |
| 55. #127 | Dic3 | semidirect |
| 56. #124 | Dic3 | semidirect |
| 165. C3 | #1910 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#535 | 2 |
| #5819 | 2 |
| #5240 | 2 |
| #5215 | 2 |
| #4531 | 2 |
| #1910 | 3 |