Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 107 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×C4⋊C4 | C2 | semidirect |
| 3. C2×C3×#102 | C2 | semidirect |
| 4. C2×#832 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C8 | C2 | semidirect |
| 6. #4551 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 17. #938 | C4 | semidirect |
| 30. C2×#102 | D3 | semidirect |
| 41. C2×C3×D4 | C2×C4 | semidirect |
| 63. C3×C4⋊C4 | D4 | semidirect |
| 67. C4⋊Dic3 | C2×C4 | semidirect |
| 68. C4⋊Dic3 | D4 | semidirect |
| 146. C2×D4 | C4×D3 | semidirect |
| 173. C4⋊C4 | #67 | semidirect |
| 195. C2×D3 | #102 | semidirect |
| 287. C3 | #1874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#938 | 2 |
| C2×D3×C4⋊C4 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| #4551 | 2 |
| #4529 | 2 |
| #1874 | 3 |