Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#137 | C2 | semidirect |
| 3. C2×#951 | C2 | semidirect |
| 4. C2×#944 | C2 | semidirect |
| 5. C2×#942 | C2 | semidirect |
| 6. C2×#909 | C2 | semidirect |
| 7. #5190 | C2 | semidirect |
| 8. #5183 | C2 | semidirect |
| 9. #5175 | C2 | semidirect |
| 10. #5167 | C2 | semidirect |
| 11. Dic3×M16 | C2 | semidirect |
| 47. C2×#137 | D3 | semidirect |
| 82. C3×M16 | D4 | semidirect |
| 96. #208 | D4 | semidirect |
| 202. M16 | #67 | semidirect |
| 228. Dic3 | #137 | semidirect |
| 287. C3 | #3152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| #5832 | 2 |
| C2×#951 | 2 |
| C2×#944 | 2 |
| C2×#942 | 2 |
| C2×#909 | 2 |
| #5190 | 2 |
| #5183 | 2 |
| #5175 | 2 |
| #5167 | 2 |
| Dic3×M16 | 2 |
| #3152 | 3 |