Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1880 conjugacy classes of subgroups; only the 901 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 901 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. C22×C3×C4⋊C4 | C2 | semidirect |
| 4. C22×C4⋊Dic3 | C2 | semidirect |
| 5. C22×C4×Dic3 | C2 | semidirect |
| 6. C2×#892 | C2 | direct (N × H) |
| 13. C22×C4×D3 | C4 | semidirect |
| 15. C2×C3×C4⋊C4 | C22 | semidirect |
| 17. C2×C4⋊Dic3 | C22 | semidirect |
| 18. C2×C4×Dic3 | C22 | semidirect |
| 19. #892 | C22 | direct (N × H) |
| 23. C22×C4⋊C4 | D3 | semidirect |
| 39. C2×C4×D3 | C2×C4 | semidirect |
| 41. C3×C4⋊C4 | C23 | semidirect |
| 43. C4⋊Dic3 | C23 | semidirect |
| 44. C4×Dic3 | C23 | semidirect |
| 54. C2×C4⋊C4 | C2×D3 | semidirect |
| 74. C4×D3 | C22×C4 | semidirect |
| 91. C4⋊C4 | C22×D3 | semidirect |
| 94. C22×C3 | #117 | semidirect |
| 125. C2×C3 | C2×#117 | semidirect |
| 134. C22 | #892 | direct (N × H) |
| 143. C3 | C22×#117 | semidirect |
| 145. C2 | C2×#892 | 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 |
| C22×C3×C4⋊C4 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×C4×Dic3 | 2 |
| C2×#892 | 2 |
| C22×#117 | 3 |