Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
596 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 181 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. #5211 | C2 | semidirect |
| 4. #4957 | C2 | semidirect |
| 5. #4956 | C2 | semidirect |
| 6. #4940 | C2 | semidirect |
| 7. C4×(C2×D3)⋊C4 | C2 | semidirect |
| 8. #4665 | C2 | semidirect |
| 9. #4654 | C2 | semidirect |
| 20. #930 | C4 | semidirect |
| 41. C4×C22⋊C4 | D3 | semidirect |
| 46. C22×C3×C4 | C2×C4 | semidirect |
| 53. C2×#67 | C2×C4 | semidirect |
| 71. (C2×D3)⋊C4 | C2×C4 | semidirect |
| 72. C4⋊Dic3 | C2×C4 | semidirect |
| 151. C22×C4 | C4×D3 | semidirect |
| 261. C3 | #2333 | 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 |
| #5211 | 2 |
| #4957 | 2 |
| #4956 | 2 |
| #4940 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4665 | 2 |
| #4654 | 2 |
| #2333 | 3 |