Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20275181 | C2 | semidirect |
| 4. #20274897 | C2 | semidirect |
| 5. #20273236 | C2 | semidirect |
| 7. C53×#1293 | C2 | semidirect |
| 220. #1293 | D53 | semidirect |
| 252. C53 | #10558 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285473 | 2 |
| #20275181 | 2 |
| #20275176 | 2 |
| #20274897 | 2 |
| #20273236 | 2 |
| #20273232 | 2 |
| C53×#1293 | 2 |
| #10558 | 53 |