Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
368 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 368 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. #20273461 | C2 | semidirect |
| 4. #20272546 | C2 | semidirect |
| 5. C53×#1275 | C2 | semidirect |
| 143. #1275 | D53 | semidirect |
| 165. C53 | #8603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810685 | 2 |
| #20273461 | 2 |
| #20273027 | 2 |
| #20272546 | 2 |
| C53×#1275 | 2 |
| #8603 | 53 |