Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
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. #28381879 | C2 | semidirect |
| 2. #28381877 | C2 | semidirect |
| 3. #28381873 | C2 | semidirect |
| 4. #28381868 | C2 | semidirect |
| 5. #28381866 | C2 | semidirect |
| 7. C4×Dic886 | C2 | semidirect |
| 8. C4×C22⋊D443 | C2 | semidirect |
| 9. #28381845 | C2 | semidirect |
| 10. C42×D443 | C2 | semidirect |
| 11. C4×D4×C443 | C2 | semidirect |
| 74. C443 | #529 | semidirect |
| 84. C4×D4 | D443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28381879 | 2 |
| #28381877 | 2 |
| #28381873 | 2 |
| #28381868 | 2 |
| #28381866 | 2 |
| #28381857 | 2 |
| C4×Dic886 | 2 |
| C4×C22⋊D443 | 2 |
| #28381845 | 2 |
| C42×D443 | 2 |
| C4×D4×C443 | 2 |
| #529 | 443 |