Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1968 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 645 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. C24×Dic3 | C2 | semidirect |
| 3. C22×C3×C22⋊C4 | C2 | semidirect |
| 4. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C22×C4⋊Dic3 | C2 | semidirect |
| 6. C2×#886 | C2 | direct (N × H) |
| 16. C23×Dic3 | C22 | semidirect |
| 17. C2×C3×C22⋊C4 | C22 | semidirect |
| 18. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 19. C2×C4⋊Dic3 | C22 | semidirect |
| 20. #886 | C22 | direct (N × H) |
| 26. C22×C22⋊C4 | D3 | semidirect |
| 43. C22×Dic3 | C23 | semidirect |
| 44. C3×C22⋊C4 | C23 | semidirect |
| 45. (C2×D3)⋊C4 | C23 | semidirect |
| 46. C4⋊Dic3 | C23 | semidirect |
| 59. C2×C22⋊C4 | C2×D3 | semidirect |
| 98. C22⋊C4 | C22×D3 | semidirect |
| 101. C22×C3 | #123 | semidirect |
| 132. C2×C3 | C2×#123 | semidirect |
| 141. C22 | #886 | direct (N × H) |
| 149. C3 | C22×#123 | semidirect |
| 152. C2 | C2×#886 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#67 | 2 |
| C24×Dic3 | 2 |
| C22×C3×C22⋊C4 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C2×#886 | 2 |
| C22×#123 | 3 |