Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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×D3×C22⋊C4 | C2 | semidirect |
| 3. C2×C3×#99 | C2 | semidirect |
| 4. C2×#834 | C2 | semidirect |
| 5. #4955 | C2 | semidirect |
| 6. #4527 | C2 | semidirect |
| 7. #4527 | C2 | semidirect |
| 11. C22×#67 | C4 | semidirect |
| 23. C2×(C2×D3)⋊C4 | C4 | semidirect |
| 31. C2×#99 | D3 | semidirect |
| 35. C24×C3 | C2×C4 | semidirect |
| 54. C22×C3×C4 | C2×C4 | semidirect |
| 60. C22×Dic3 | C2×C4 | semidirect |
| 66. C3×C22⋊C4 | D4 | semidirect |
| 72. #217 | D4 | semidirect |
| 157. C24 | C4×D3 | semidirect |
| 175. C22×C4 | C4×D3 | semidirect |
| 189. C22⋊C4 | #67 | semidirect |
| 221. C2×D3 | #99 | semidirect |
| 329. C3 | #1898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#937 | 2 |
| C2×D3×C22⋊C4 | 2 |
| C2×C3×#99 | 2 |
| C2×#834 | 2 |
| #4955 | 2 |
| #4527 | 2 |
| #1898 | 3 |