Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #13050159 | C2 | semidirect |
| 2. #13050157 | C2 | semidirect |
| 3. #13050154 | C2 | semidirect |
| 4. #13050150 | C2 | semidirect |
| 5. #13050148 | C2 | semidirect |
| 6. #13050145 | C2 | semidirect |
| 7. #13050141 | C2 | semidirect |
| 9. C4×Dic82 | C2 | semidirect |
| 10. C4×C22⋊D41 | C2 | semidirect |
| 11. C4×C22⋊D41 | C2 | semidirect |
| 12. #13050123 | C2 | semidirect |
| 13. #13050121 | C2 | semidirect |
| 14. C2×C4×Dic41 | C2 | semidirect |
| 15. C4×D4×C41 | C2 | semidirect |
| 104. C41 | #529 | semidirect |
| 116. C4×D4 | D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050159 | 2 |
| #13050157 | 2 |
| #13050154 | 2 |
| #13050150 | 2 |
| #13050148 | 2 |
| #13050145 | 2 |
| #13050141 | 2 |
| #13050136 | 2 |
| C4×Dic82 | 2 |
| C4×C22⋊D41 | 2 |
| #13050123 | 2 |
| #13050121 | 2 |
| C2×C4×Dic41 | 2 |
| C4×D4×C41 | 2 |
| #529 | 41 |