Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #28381880 | C2 | semidirect |
| 2. #28381878 | C2 | semidirect |
| 3. #28381874 | C2 | semidirect |
| 4. #28381869 | C2 | semidirect |
| 5. #28381865 | C2 | semidirect |
| 7. C4×Dic886 | C2 | semidirect |
| 8. C4×D1772 | C2 | semidirect |
| 9. C4×C22⋊D443 | C2 | semidirect |
| 10. #28381843 | C2 | semidirect |
| 11. C2×C42×C443 | C2 | semidirect |
| 74. C443 | #529 | semidirect |
| 86. C2×C42 | D443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28381880 | 2 |
| #28381878 | 2 |
| #28381874 | 2 |
| #28381869 | 2 |
| #28381865 | 2 |
| #28381860 | 2 |
| C4×Dic886 | 2 |
| C4×D1772 | 2 |
| C4×C22⋊D443 | 2 |
| #28381843 | 2 |
| C2×C42×C443 | 2 |
| #529 | 443 |