Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
330 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#16810445 | C2 | semidirect |
| 4. #20272797 | C2 | semidirect |
| 5. C53×#1846 | C2 | semidirect |
| 110. #1846 | D53 | semidirect |
| 128. C53 | #13534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810445 | 2 |
| C2×#16810432 | 2 |
| #20275603 | 2 |
| #20272797 | 2 |
| C53×#1846 | 2 |
| #13534 | 53 |