Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #20289704 | C2 | semidirect |
| 4. #20289703 | C2 | semidirect |
| 12. C2×Q16×D53 | C4 | semidirect |
| 16. #16810864 | C4 | semidirect |
| 20. #107×D53 | C4 | semidirect |
| 22. C53×#467 | C4 | semidirect |
| 182. #467 | #6157 | semidirect |
| 190. C53 | #11889 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290944 | 2 |
| #20290591 | 2 |
| #20289704 | 2 |
| #20289703 | 2 |
| #467×D53 | 2 |
| #11889 | 53 |