Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
736 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 161 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×#10625120 | C2 | semidirect |
| 2. #13092981 | C2 | semidirect |
| 3. #13092590 | C2 | semidirect |
| 4. #13092585 | C2 | semidirect |
| 5. #13092434 | C2 | semidirect |
| 6. #13092401 | C2 | semidirect |
| 7. C23×#585 | C2 | semidirect |
| 9. C23×2−1+4 | C22 | semidirect |
| 12. C23×H(5,𝔽2) | C22 | semidirect |
| 17. C22×D92 | C22 | semidirect |
| 19. #10625120 | C22 | semidirect |
| 20. #10625118 | C22 | semidirect |
| 22. #10625111 | C22 | semidirect |
| 26. #10625097 | C22 | semidirect |
| 27. C2×#67267 | C22 | semidirect |
| 28. #10625019 | C22 | semidirect |
| 29. #10625018 | C22 | semidirect |
| 30. #10625015 | C22 | semidirect |
| 42. #41×C23 | D4 | semidirect |
| 46. C2×Q8×C23 | D4 | semidirect |
| 54. C2×D4×C23 | D4 | semidirect |
| 129. #585 | D23 | semidirect |
| 143. 2−1+4 | C2×D23 | semidirect |
| 146. H(5,𝔽2) | C2×D23 | semidirect |
| 165. C23 | #3021 | semidirect |
| 177. #41 | C22⋊D23 | semidirect |
| 181. C2×Q8 | C22⋊D23 | semidirect |
| 194. C2×D4 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625120 | 2 |
| #13092981 | 2 |
| #13092590 | 2 |
| #13092585 | 2 |
| #13092434 | 2 |
| #13092401 | 2 |
| C23×#585 | 2 |
| #3021 | 23 |