Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
176 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20272914 | C2 | semidirect |
| 4. #20272897 | C2 | semidirect |
| 5. #20272895 | C2 | semidirect |
| 7. C53×#1423 | C2 | semidirect |
| 84. #1423 | D53 | semidirect |
| 103. C53 | #13715 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276807 | 2 |
| #366×D53 | 2 |
| #20272914 | 2 |
| #20272897 | 2 |
| #20272895 | 2 |
| #20272852 | 2 |
| C53×#1423 | 2 |
| #13715 | 53 |