Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 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. #13093216 | C2 | semidirect |
| 2. C2×#10625090 | C2 | semidirect |
| 3. #131×D23 | C2 | semidirect |
| 4. #13092689 | C2 | semidirect |
| 5. #13092688 | C2 | semidirect |
| 6. #13092687 | C2 | semidirect |
| 7. #13092683 | C2 | semidirect |
| 8. #13092682 | C2 | semidirect |
| 9. #108×D23 | C2 | semidirect |
| 10. #13092400 | C2 | semidirect |
| 11. C23×#473 | C2 | semidirect |
| 15. C2×Q16×C23 | C22 | semidirect |
| 20. C2×#67274 | C22 | semidirect |
| 35. C2×D184 | C22 | semidirect |
| 40. C23×#108 | C22 | semidirect |
| 41. C23×#101 | C22 | semidirect |
| 42. #10625018 | C22 | semidirect |
| 43. #10625005 | C22 | semidirect |
| 44. #10625005 | C22 | semidirect |
| 45. #10625004 | C22 | semidirect |
| 46. #10625001 | C22 | semidirect |
| 164. #473 | D23 | semidirect |
| 192. C2×Q16 | C2×D23 | semidirect |
| 208. #108 | C2×D23 | semidirect |
| 210. #101 | C2×D23 | semidirect |
| 213. C23 | #3067 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13093216 | 2 |
| C2×#10625090 | 2 |
| #131×D23 | 2 |
| #13092689 | 2 |
| #13092688 | 2 |
| #13092687 | 2 |
| #13092683 | 2 |
| #13092682 | 2 |
| #108×D23 | 2 |
| #13092400 | 2 |
| C23×#473 | 2 |
| #3067 | 23 |