Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#1007 | C2 | semidirect |
| 2. C2×C3×#137 | C2 | semidirect |
| 3. #5833 | C2 | semidirect |
| 4. C2×#950 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 6. #5187 | C2 | semidirect |
| 7. #5186 | C2 | semidirect |
| 8. #5172 | C2 | semidirect |
| 9. #5170 | C2 | semidirect |
| 10. #5133 | C2 | semidirect |
| 11. #5129 | C2 | semidirect |
| 47. C2×#137 | D3 | semidirect |
| 61. C2×C3×Q8 | D4 | semidirect |
| 83. #235 | D4 | semidirect |
| 204. C2×Q8 | #67 | semidirect |
| 331. C3 | #3013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1007 | 2 |
| C2×C3×#137 | 2 |
| #5833 | 2 |
| C2×#950 | 2 |
| C2×#835 | 2 |
| #5187 | 2 |
| #5186 | 2 |
| #5172 | 2 |
| #5170 | 2 |
| #5133 | 2 |
| #5129 | 2 |
| #3013 | 3 |