Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
548 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20277686 | C2 | semidirect |
| 3. #20273275 | C2 | semidirect |
| 4. #20273105 | C2 | semidirect |
| 5. #20272618 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1502 | C2 | semidirect |
| 11. #16810825 | C4 | semidirect |
| 12. #16810815 | C4 | semidirect |
| 206. #1502 | D53 | semidirect |
| 238. C53 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284175 | 2 |
| #20277686 | 2 |
| #20273275 | 2 |
| #20273105 | 2 |
| #20272618 | 2 |
| #20272574 | 2 |
| C53×#1502 | 2 |
| #9181 | 53 |