Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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. C2×C3×#117 | C2 | semidirect |
| 3. C22×#208 | C2 | semidirect |
| 4. #5001 | C2 | direct (N × H) |
| 5. C2×#809 | C2 | semidirect |
| 12. C22×D12 | C4 | semidirect |
| 16. C3×#117 | C22 | semidirect |
| 17. C2×C3×C4⋊C4 | C22 | semidirect |
| 21. C2×#208 | C22 | semidirect |
| 22. C22×C3⋊C8 | C22 | semidirect |
| 23. #809 | C22 | semidirect |
| 26. C2×#117 | D3 | semidirect |
| 48. C2×D12 | C2×C4 | semidirect |
| 51. C3×C4⋊C4 | C23 | semidirect |
| 56. C2×C3⋊C8 | C23 | semidirect |
| 69. #117 | C2×D3 | semidirect |
| 70. C2×C4⋊C4 | C2×D3 | semidirect |
| 125. C4⋊C4 | C22×D3 | semidirect |
| 170. C2×C3 | #418 | semidirect |
| 189. C3 | C2×#418 | semidirect |
| 192. C2 | #5001 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D12 | 2 |
| C2×C3×#117 | 2 |
| C22×#208 | 2 |
| #5001 | 2 |
| C2×#809 | 2 |
| C2×#418 | 3 |