Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #20273467 | C2 | semidirect |
| 5. #20273405 | C2 | semidirect |
| 6. #20272618 | C2 | semidirect |
| 7. C53×#1986 | C2 | semidirect |
| 92. M16×C53 | SD16 | semidirect |
| 186. #1986 | D53 | semidirect |
| 219. C53 | #10504 | semidirect |
| 287. M16 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285653 | 2 |
| #20275642 | 2 |
| #20275555 | 2 |
| #20273467 | 2 |
| #20273405 | 2 |
| #20272618 | 2 |
| C53×#1986 | 2 |
| #10504 | 53 |