Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
712 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20276231 | C2 | semidirect |
| 2. #20276114 | C2 | semidirect |
| 3. #20276112 | C2 | semidirect |
| 5. C53×#2091 | C2 | semidirect |
| 7. #16810672 | C22 | semidirect |
| 8. #16810671 | C22 | semidirect |
| 12. #16810381 | C22 | semidirect |
| 13. C53×#430 | C22 | semidirect |
| 15. C53×#338 | C22 | semidirect |
| 84. #2091 | D53 | semidirect |
| 95. #430 | C2×D53 | semidirect |
| 101. #338 | C2×D53 | semidirect |
| 102. C53 | #32875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276231 | 2 |
| #20276114 | 2 |
| #20276112 | 2 |
| #20274635 | 2 |
| C53×#2091 | 2 |
| #32875 | 53 |