Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C2×#20296771 | C2 | semidirect |
| 3. #28381814 | C2 | direct (N × H) |
| 4. C2×C42×C443 | C2 | semidirect |
| 7. #20296787 | C4 | semidirect |
| 9. C2×Dic886 | C4 | semidirect |
| 10. C2×D1772 | C4 | semidirect |
| 14. #20296771 | C22 | semidirect |
| 19. C42×C443 | C22 | semidirect |
| 22. Dic886 | C2×C4 | semidirect |
| 24. D1772 | C2×C4 | semidirect |
| 54. C2×C443 | #104 | semidirect |
| 57. C443 | C2×#104 | semidirect |
| 61. C2×C42 | D443 | semidirect |
| 77. C42 | C2×D443 | semidirect |
| 113. C2 | #28381814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20296787 | 2 |
| C2×#20296771 | 2 |
| #28381814 | 2 |
| C2×C42×C443 | 2 |
| C2×#104 | 443 |