Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1840 conjugacy classes of subgroups; only the 685 normal subgroups are shown.
This group has 1840 conjugacy classes of subgroups — too many to draw. Only its 685 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. C23×Dic6 | C2 | semidirect |
| 3. C22×C3×C4⋊C4 | C2 | semidirect |
| 5. C22×C4⋊Dic3 | C2 | semidirect |
| 6. C2×#897 | C2 | direct (N × H) |
| 16. C22×Dic6 | C22 | semidirect |
| 17. C2×C3×C4⋊C4 | C22 | semidirect |
| 19. C2×C4⋊Dic3 | C22 | semidirect |
| 20. #897 | C22 | direct (N × H) |
| 25. C22×C4⋊C4 | D3 | semidirect |
| 30. C23×D3 | Q8 | semidirect |
| 43. C2×Dic6 | C23 | semidirect |
| 44. C3×C4⋊C4 | C23 | semidirect |
| 46. C4⋊Dic3 | C23 | semidirect |
| 58. C2×C4⋊C4 | C2×D3 | semidirect |
| 67. C22×D3 | C2×Q8 | semidirect |
| 97. C4⋊C4 | C22×D3 | semidirect |
| 99. C22×C3 | C22⋊Q8 | semidirect |
| 107. C2×D3 | C22×Q8 | semidirect |
| 131. C2×C3 | C2×C22⋊Q8 | semidirect |
| 140. C22 | #897 | direct (N × H) |
| 149. C3 | C22×C22⋊Q8 | semidirect |
| 151. C2 | C2×#897 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D3 | 2 |
| C23×Dic6 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C2×#897 | 2 |
| C22×C22⋊Q8 | 3 |