Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 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. #5236 | C2 | semidirect |
| 5. #4523 | C2 | semidirect |
| 9. C3×C4⋊Q8 | C4 | semidirect |
| 10. C3×#127 | C4 | semidirect |
| 11. C3×#124 | C4 | semidirect |
| 12. C3×#124 | C4 | semidirect |
| 53. #208 | D4 | semidirect |
| 61. C4⋊Q8 | Dic3 | semidirect |
| 62. #127 | Dic3 | semidirect |
| 63. #124 | Dic3 | semidirect |
| 64. #124 | Dic3 | semidirect |
| 185. C3 | #1884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| #5819 | 2 |
| #5240 | 2 |
| #5236 | 2 |
| #4523 | 2 |
| #1884 | 3 |