Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #20283350 | C2 | semidirect |
| 3. #20275563 | C2 | semidirect |
| 4. #20275553 | C2 | semidirect |
| 5. #20274643 | C2 | semidirect |
| 6. #20274635 | C2 | semidirect |
| 7. C53×#1785 | C2 | semidirect |
| 16. #16810646 | C22 | semidirect |
| 17. C2×#13133136 | C22 | semidirect |
| 18. C2×#13133134 | C22 | semidirect |
| 22. M16×Dic53 | C22 | semidirect |
| 24. C2×#101×C53 | C22 | semidirect |
| 25. C2×#100×C53 | C22 | semidirect |
| 180. #1785 | D53 | semidirect |
| 200. C2×#101 | C2×D53 | semidirect |
| 204. C2×#100 | C2×D53 | semidirect |
| 208. C53 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811187 | 2 |
| #20283350 | 2 |
| #20275563 | 2 |
| #20275553 | 2 |
| #20274643 | 2 |
| #20274635 | 2 |
| C53×#1785 | 2 |
| #21801 | 53 |