Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
257 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#6913⋊C2 | C2 | semidirect |
| 2. C4×#6913 | C2 | semidirect |
| 3. C4⋊#4208 | C3 | semidirect |
| 5. C4⋊#4178 | C3 | semidirect |
| 6. C4⋊#4176 | C3 | semidirect |
| 7. C4⋊#4174 | C3 | semidirect |
| 10. C2×#4208 | C2×C3 | semidirect |
| 13. C4×#737 | C2×C3 | semidirect |
| 14. C3×C4×3−1+2 | D3 | semidirect |
| 15. C2×#4178 | C2×C3 | semidirect |
| 16. C2×#4176 | C2×C3 | semidirect |
| 19. C4×#732 | C2×C3 | semidirect |
| 21. C4×#731 | C2×C3 | semidirect |
| 24. #6913 | D4 | semidirect |
| 70. #737 | C3×D4 | semidirect |
| 71. C3×3−1+2 | D12 | semidirect |
| 73. #732 | C3×D4 | semidirect |
| 75. #731 | C3×D4 | semidirect |
| 198. C4 | #6913⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6913⋊C2 | 2 |
| C4×#6913 | 2 |
| C4⋊#4208 | 3 |
| D12×3−1+2 | 3 |
| C4⋊#4178 | 3 |
| C4⋊#4176 | 3 |
| C4⋊#4174 | 3 |