Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #13093234 | C2 | semidirect |
| 2. #13093227 | C2 | semidirect |
| 3. #13093218 | C2 | semidirect |
| 4. #13092800 | C2 | semidirect |
| 5. #13092693 | C2 | semidirect |
| 6. #13092679 | C2 | semidirect |
| 7. #13092597 | C2 | semidirect |
| 8. #13092588 | C2 | semidirect |
| 9. #13092533 | C2 | semidirect |
| 10. #13092532 | C2 | semidirect |
| 11. C23×#472 | C2 | semidirect |
| 12. #10625161 | C22 | semidirect |
| 14. C23×AGL(1,ℤ/8) | C22 | semidirect |
| 16. C23×#131 | C22 | semidirect |
| 18. #10625107 | C22 | semidirect |
| 19. C2×#67273 | C22 | semidirect |
| 30. #10625080 | C22 | semidirect |
| 31. #10625078 | C22 | semidirect |
| 33. C2×Dic92 | C22 | semidirect |
| 37. C23×#108 | C22 | semidirect |
| 38. C23×#100 | C22 | semidirect |
| 39. #10625019 | C22 | semidirect |
| 41. #10625007 | C22 | semidirect |
| 42. #10625006 | C22 | semidirect |
| 43. #10625004 | C22 | semidirect |
| 44. C8×Dic23 | C22 | semidirect |
| 149. #472 | D23 | semidirect |
| 170. AGL(1,ℤ/8) | C2×D23 | semidirect |
| 184. #131 | C2×D23 | semidirect |
| 187. #108 | C2×D23 | semidirect |
| 192. #100 | C2×D23 | semidirect |
| 194. C23 | #3290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093234 | 2 |
| #13093227 | 2 |
| #13093218 | 2 |
| #13092800 | 2 |
| #13092693 | 2 |
| #13092679 | 2 |
| #13092597 | 2 |
| #13092588 | 2 |
| #13092533 | 2 |
| #13092532 | 2 |
| C23×#472 | 2 |
| #3290 | 23 |