Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#10625161 | C2 | semidirect |
| 2. #13093215 | C2 | semidirect |
| 3. #13092988 | C2 | semidirect |
| 4. #13092598 | C2 | semidirect |
| 5. #13092588 | C2 | semidirect |
| 6. #13092434 | C2 | semidirect |
| 7. #13092433 | C2 | semidirect |
| 8. C2×#10625006 | C2 | semidirect |
| 9. C23×#575 | C2 | semidirect |
| 24. C23×#137 | C22 | semidirect |
| 26. C23×AGL(1,ℤ/8) | C22 | semidirect |
| 32. #10625115 | C22 | semidirect |
| 33. #10625113 | C22 | semidirect |
| 34. #10625107 | C22 | semidirect |
| 36. #10625103 | C22 | semidirect |
| 40. #10625019 | C22 | semidirect |
| 41. #10625007 | C22 | semidirect |
| 42. #10625006 | C22 | semidirect |
| 181. #575 | D23 | semidirect |
| 211. #137 | C2×D23 | semidirect |
| 215. AGL(1,ℤ/8) | C2×D23 | semidirect |
| 228. C23 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625161 | 2 |
| #13093215 | 2 |
| #13092988 | 2 |
| #13092598 | 2 |
| #13092588 | 2 |
| #13092434 | 2 |
| #13092433 | 2 |
| C2×#10625006 | 2 |
| C23×#575 | 2 |
| #3020 | 23 |