Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
878 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20291037 | C2 | semidirect |
| 2. #20291025 | C2 | semidirect |
| 3. #20290952 | C2 | semidirect |
| 4. #20290597 | C2 | semidirect |
| 20. C2×#13133240 | C4 | semidirect |
| 22. C2×#13133239 | C4 | semidirect |
| 23. C2×Q16×D53 | C4 | semidirect |
| 26. C22×Q16×C53 | C4 | semidirect |
| 241. C22×Q16 | #6157 | semidirect |
| 251. C53 | #12742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291037 | 2 |
| #20291025 | 2 |
| #20290952 | 2 |
| #20290597 | 2 |
| C2×#16811436 | 2 |
| #12742 | 53 |