Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#947 | C2 | semidirect |
| 4. C2×#837 | C2 | semidirect |
| 5. #5225 | C2 | semidirect |
| 6. C2×#823 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 30. C2×#137 | D3 | semidirect |
| 48. C2×C3×Q8 | D4 | semidirect |
| 65. C3×M16 | D4 | semidirect |
| 73. C4×Dic3 | D4 | semidirect |
| 147. C2×Q8 | #67 | semidirect |
| 166. M16 | #67 | semidirect |
| 256. C3 | #2004 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| #5830 | 2 |
| C2×#947 | 2 |
| C2×#837 | 2 |
| #5225 | 2 |
| C2×#823 | 2 |
| #4555 | 2 |
| #2004 | 3 |