Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 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. #13093070 | C2 | semidirect |
| 2. #13093052 | C2 | semidirect |
| 3. #13092729 | C2 | semidirect |
| 4. #13092694 | C2 | semidirect |
| 5. #13092652 | C2 | semidirect |
| 6. #13092609 | C2 | semidirect |
| 7. #13092552 | C2 | semidirect |
| 8. C4×D184 | C2 | semidirect |
| 9. C8×D92 | C2 | semidirect |
| 10. #102×D23 | C2 | semidirect |
| 11. C23×#486 | C2 | semidirect |
| 15. C23×C4⋊Q8 | C22 | semidirect |
| 21. C2×#67272 | C22 | semidirect |
| 23. C2×C8×D23 | C22 | semidirect |
| 24. #10625066 | C22 | semidirect |
| 26. C4⋊C4×D23 | C22 | semidirect |
| 29. C4×D92 | C22 | semidirect |
| 30. C23×#102 | C22 | semidirect |
| 31. C23×#102 | C22 | semidirect |
| 32. C4×C8×C23 | C22 | semidirect |
| 33. #10625014 | C22 | semidirect |
| 35. #10625003 | C22 | semidirect |
| 36. (C2×D23)⋊C8 | C22 | semidirect |
| 37. #10625000 | C22 | semidirect |
| 39. #10624989 | C22 | semidirect |
| 40. C4⋊(C23⋊C8) | C22 | semidirect |
| 103. D92 | D8 | semidirect |
| 104. D92 | #41 | semidirect |
| 138. #486 | D23 | semidirect |
| 160. C4⋊Q8 | C2×D23 | semidirect |
| 179. #102 | C2×D23 | semidirect |
| 180. #102 | C2×D23 | semidirect |
| 182. C4×C8 | C2×D23 | semidirect |
| 183. C23 | #3294 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093070 | 2 |
| #13093052 | 2 |
| #13092729 | 2 |
| #13092694 | 2 |
| #13092652 | 2 |
| #13092609 | 2 |
| #13092552 | 2 |
| C4×D184 | 2 |
| C8×D92 | 2 |
| #102×D23 | 2 |
| C23×#486 | 2 |
| #3294 | 23 |