Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
1880 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 661 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×C3×#95 | C2 | semidirect |
| 3. C2×C3⋊#95 | C2 | semidirect |
| 4. D3×#95 | C2 | direct (N × H) |
| 10. C22×C4×D3 | C4 | semidirect |
| 12. C3×#95 | C22 | semidirect |
| 13. C3⋊#95 | C22 | semidirect |
| 17. C2×#95 | D3 | direct (N × H) |
| 24. C22×C3×C4 | C2×C4 | semidirect |
| 27. C22×Dic3 | C2×C4 | semidirect |
| 31. C2×C4×D3 | C2×C4 | semidirect |
| 39. #95 | C2×D3 | direct (N × H) |
| 52. C2×C3×C4 | C22×C4 | semidirect |
| 55. C2×Dic3 | C22×C4 | semidirect |
| 69. C22×C4 | C4×D3 | semidirect |
| 77. C2×D3 | #95 | direct (N × H) |
| 99. C2×C4 | C2×C4×D3 | semidirect |
| 100. C2×C3 | C2×#95 | semidirect |
| 104. D3 | C2×#95 | direct (N × H) |
| 117. C3 | C22×#95 | semidirect |
| 119. C2 | D3×#95 | 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 |
| C2×C3×#95 | 2 |
| C2×C3⋊#95 | 2 |
| D3×#95 | 2 |
| C22×#95 | 3 |