Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10625122 | C2 | semidirect |
| 2. C2×#10625103 | C2 | semidirect |
| 3. C2×#10625121 | C2 | semidirect |
| 4. C22×#67273 | C2 | semidirect |
| 5. #13092993 | C2 | semidirect |
| 6. #13092812 | C2 | semidirect |
| 7. #13092804 | C2 | semidirect |
| 8. #13092799 | C2 | semidirect |
| 9. #13092789 | C2 | semidirect |
| 10. #13092373 | C2 | semidirect |
| 11. C23×#535 | C2 | semidirect |
| 23. C2×#67275 | C22 | semidirect |
| 24. C2×#67275 | C22 | semidirect |
| 25. C2×#67274 | C22 | semidirect |
| 30. C2×#67273 | C22 | semidirect |
| 31. C2×#67273 | C22 | semidirect |
| 34. C2×#67272 | C22 | semidirect |
| 39. #10625046 | C22 | semidirect |
| 40. #10625040 | C22 | semidirect |
| 41. #10624985 | C22 | semidirect |
| 42. C4×C23⋊C8 | C22 | semidirect |
| 83. #67267 | D4 | semidirect |
| 84. C2×C23⋊C8 | D4 | semidirect |
| 148. #535 | D23 | semidirect |
| 191. C23 | #3154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625122 | 2 |
| C2×#10625103 | 2 |
| C2×#10625121 | 2 |
| C22×#67273 | 2 |
| #13092993 | 2 |
| #13092812 | 2 |
| #13092804 | 2 |
| #13092799 | 2 |
| #13092789 | 2 |
| #13092373 | 2 |
| C23×#535 | 2 |
| #3154 | 23 |