Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
630 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275709 | C2 | semidirect |
| 3. #20273446 | C2 | semidirect |
| 6. #20273135 | C2 | semidirect |
| 7. C53×#1470 | C2 | semidirect |
| 237. #1470 | D53 | semidirect |
| 272. C53 | #8485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289321 | 2 |
| #20275709 | 2 |
| #20273446 | 2 |
| #20273323 | 2 |
| #20273181 | 2 |
| #20273135 | 2 |
| C53×#1470 | 2 |
| #8485 | 53 |