Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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. #13093127 | C2 | semidirect |
| 3. #13092763 | C2 | semidirect |
| 4. #13092734 | C2 | semidirect |
| 5. #13092708 | C2 | semidirect |
| 6. #13092643 | C2 | semidirect |
| 7. #13092566 | C2 | semidirect |
| 8. C4×#67274 | C2 | semidirect |
| 9. #13092482 | C2 | semidirect |
| 10. #102×D23 | C2 | semidirect |
| 11. C23×#460 | C2 | semidirect |
| 14. C2×SD16×C23 | C22 | semidirect |
| 16. C4×Q8×C23 | C22 | semidirect |
| 17. #10625117 | C22 | semidirect |
| 22. C2×C8×D23 | C22 | semidirect |
| 24. C4⋊C4×D23 | C22 | semidirect |
| 29. #10625040 | C22 | semidirect |
| 30. C23×C4⋊C8 | C22 | semidirect |
| 31. C23×#102 | C22 | semidirect |
| 32. #10625017 | C22 | semidirect |
| 33. #10625014 | C22 | semidirect |
| 34. #10625014 | C22 | semidirect |
| 36. (C2×D23)⋊C8 | C22 | semidirect |
| 37. #10624999 | C22 | semidirect |
| 39. #10624990 | C22 | semidirect |
| 40. C4×C23⋊C8 | C22 | semidirect |
| 100. D92 | SD16 | semidirect |
| 137. #460 | D23 | semidirect |
| 151. C2×SD16 | C2×D23 | semidirect |
| 161. C4×Q8 | C2×D23 | semidirect |
| 168. C4⋊C8 | C2×D23 | semidirect |
| 174. #102 | C2×D23 | semidirect |
| 177. C23 | #3295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093127 | 2 |
| #13093052 | 2 |
| #13092763 | 2 |
| #13092734 | 2 |
| #13092708 | 2 |
| #13092643 | 2 |
| #13092566 | 2 |
| C4×#67274 | 2 |
| #13092482 | 2 |
| #102×D23 | 2 |
| C23×#460 | 2 |
| #3295 | 23 |