Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #28381934 | C2 | semidirect |
| 2. #28381933 | C2 | semidirect |
| 3. #28381919 | C2 | semidirect |
| 4. #28381918 | C2 | semidirect |
| 5. #28381915 | C2 | semidirect |
| 6. #28381907 | C2 | semidirect |
| 7. #28381906 | C2 | semidirect |
| 8. C2×#20296777 | C2 | semidirect |
| 9. Q16×D443 | C2 | semidirect |
| 10. #28381894 | C2 | semidirect |
| 11. #137×C443 | C2 | semidirect |
| 87. C443 | #578 | semidirect |
| 94. #137 | D443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28381934 | 2 |
| #28381933 | 2 |
| #28381919 | 2 |
| #28381918 | 2 |
| #28381915 | 2 |
| #28381907 | 2 |
| #28381906 | 2 |
| C2×#20296777 | 2 |
| Q16×D443 | 2 |
| #28381894 | 2 |
| #137×C443 | 2 |
| #578 | 443 |