Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 77 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. C3×C4×C22⋊C4 | C2 | semidirect |
| 3. #5207 | C2 | semidirect |
| 4. #4451 | C2 | semidirect |
| 8. C22×D12 | C4 | semidirect |
| 13. #930 | C4 | semidirect |
| 16. C2×C4⋊Dic3 | C4 | semidirect |
| 18. C3×#95 | C22 | semidirect |
| 20. #830 | C22 | semidirect |
| 23. C4×C22⋊C4 | D3 | semidirect |
| 64. #95 | C2×D3 | semidirect |
| 199. C3 | #1507 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#930 | 2 |
| C3×C4×C22⋊C4 | 2 |
| #5207 | 2 |
| #4451 | 2 |
| #1507 | 3 |