Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 1. C2×C3×#135 | C2 | semidirect |
| 2. #5834 | C2 | semidirect |
| 3. C2×#919 | C2 | semidirect |
| 4. #5238 | C2 | semidirect |
| 5. Dic3×Q16 | C2 | semidirect |
| 6. #5172 | C2 | semidirect |
| 7. #5163 | C2 | semidirect |
| 8. #5157 | C2 | semidirect |
| 9. #5151 | C2 | semidirect |
| 10. #5115 | C2 | semidirect |
| 11. C8×#67 | C2 | semidirect |
| 43. C2×#135 | D3 | semidirect |
| 71. C3×Q16 | D4 | semidirect |
| 173. Q16 | #67 | semidirect |
| 214. Dic3 | #135 | semidirect |
| 277. C3 | #3287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#135 | 2 |
| #5834 | 2 |
| C2×#919 | 2 |
| #5238 | 2 |
| Dic3×Q16 | 2 |
| #5172 | 2 |
| #5163 | 2 |
| #5157 | 2 |
| #5151 | 2 |
| #5115 | 2 |
| C8×#67 | 2 |
| #3287 | 3 |