Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #13050252 | C2 | semidirect |
| 2. #13050251 | C2 | semidirect |
| 3. #13050235 | C2 | semidirect |
| 4. #13050229 | C2 | semidirect |
| 5. #13050228 | C2 | semidirect |
| 6. #13050218 | C2 | semidirect |
| 18. SD16×C41 | C4 | semidirect |
| 19. #10620285 | C4 | semidirect |
| 20. #10620282 | C4 | semidirect |
| 21. #10620273 | C4 | semidirect |
| 52. C41 | #444 | semidirect |
| 64. SD16 | #4223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050252 | 2 |
| #13050251 | 2 |
| #13050235 | 2 |
| #13050229 | 2 |
| #13050228 | 2 |
| #13050218 | 2 |
| #13050185 | 2 |
| #444 | 41 |