Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 201 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. #20275430 | C2 | semidirect |
| 4. #20275269 | C2 | semidirect |
| 6. #20274860 | C2 | semidirect |
| 7. C53×#1843 | C2 | semidirect |
| 117. #1843 | D53 | semidirect |
| 140. C53 | #23381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278013 | 2 |
| #20275430 | 2 |
| #20275320 | 2 |
| #20275269 | 2 |
| #20274896 | 2 |
| #20274860 | 2 |
| C53×#1843 | 2 |
| #23381 | 53 |