Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1386 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 243 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. #20283344 | C2 | semidirect |
| 3. #20275563 | C2 | semidirect |
| 4. #20274639 | C2 | semidirect |
| 6. C53×#1784 | C2 | semidirect |
| 16. #16810646 | C22 | semidirect |
| 17. C2×#13133136 | C22 | semidirect |
| 20. M16×Dic53 | C22 | semidirect |
| 22. C2×#101×C53 | C22 | semidirect |
| 153. #1784 | D53 | semidirect |
| 172. C2×#101 | C2×D53 | semidirect |
| 177. C53 | #21798 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133206 | 2 |
| #20283344 | 2 |
| #20275563 | 2 |
| #20274639 | 2 |
| #20274635 | 2 |
| C53×#1784 | 2 |
| #21798 | 53 |