Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #20272851 | C2 | semidirect |
| 4. #20272850 | C2 | semidirect |
| 5. C53×#1398 | C2 | semidirect |
| 10. #16810456 | C4 | semidirect |
| 11. C32×D53 | C4 | semidirect |
| 75. #1398 | D53 | semidirect |
| 90. C53 | #13551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M64×D53 | 2 |
| #20276313 | 2 |
| #20272851 | 2 |
| #20272850 | 2 |
| C53×#1398 | 2 |
| #13551 | 53 |