Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1968 conjugacy classes of subgroups; only the 605 normal subgroups are shown.
This group has 1968 conjugacy classes of subgroups — too many to draw. Only its 605 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×C4×D3 | C2 | semidirect |
| 3. C22×C3×C4⋊C4 | C2 | semidirect |
| 4. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C22×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C22×Dic3⋊C4 | C2 | semidirect |
| 8. C2×#894 | C2 | direct (N × H) |
| 20. C22×C4×D3 | C22 | semidirect |
| 21. C2×C3×C4⋊C4 | C22 | semidirect |
| 22. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 23. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D3)⋊C4 | C22 | semidirect |
| 25. C2×Dic3⋊C4 | C22 | semidirect |
| 26. #894 | C22 | direct (N × H) |
| 31. C22×C4⋊C4 | D3 | semidirect |
| 57. C2×C4×D3 | C23 | semidirect |
| 58. C3×C4⋊C4 | C23 | semidirect |
| 59. (C2×D3)⋊C4 | C23 | semidirect |
| 60. (C2×D3)⋊C4 | C23 | semidirect |
| 61. (C2×D3)⋊C4 | C23 | semidirect |
| 62. Dic3⋊C4 | C23 | semidirect |
| 76. C2×C4⋊C4 | C2×D3 | semidirect |
| 130. C4⋊C4 | C22×D3 | semidirect |
| 134. C22×C3 | #123 | semidirect |
| 178. C2×C3 | C2×#123 | semidirect |
| 192. C22 | #894 | direct (N × H) |
| 202. C3 | C22×#123 | semidirect |
| 205. C2 | C2×#894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D12 | 2 |
| C23×C4×D3 | 2 |
| C22×C3×C4⋊C4 | 2 |
| C22×(C2×D3)⋊C4 | 2 |
| C22×Dic3⋊C4 | 2 |
| C2×#894 | 2 |
| C22×#123 | 3 |