Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1196 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1196 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 1. C22×3−1+4 | C2 | semidirect |
| 2. C2×#92394 | C2 | direct (N × H) |
| 3. C22×#4208 | C3 | semidirect |
| 6. C2×3−1+4 | C22 | semidirect |
| 7. #92394 | C22 | direct (N × H) |
| 9. C22×#737 | C2×C3 | semidirect |
| 11. C22×C3×3−1+2 | D3 | semidirect |
| 13. C2×#4208 | C2×C3 | semidirect |
| 16. 3−1+4 | C23 | semidirect |
| 22. C2×#737 | C22×C3 | semidirect |
| 24. C2×C3×3−1+2 | C2×D3 | semidirect |
| 26. #4208 | C22×C3 | semidirect |
| 40. C22×C3×C9 | C3×D3 | semidirect |
| 44. #737 | C23×C3 | semidirect |
| 46. C3×3−1+2 | C22×D3 | semidirect |
| 63. C2×C3×C9 | C2×C3×D3 | semidirect |
| 85. C3×C9 | C22×C3×D3 | semidirect |
| 121. C22 | #92394 | direct (N × H) |
| 127. C2 | C2×#92394 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×3−1+4 | 2 |
| C2×#92394 | 2 |
| C22×#4208 | 3 |
| C22×C3×#272 | 3 |
| C22×D3×3−1+2 | 3 |