Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
636 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 151 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. #20287868 | C2 | semidirect |
| 2. #20286520 | C2 | semidirect |
| 3. #20276968 | C2 | semidirect |
| 4. #20276840 | C2 | semidirect |
| 5. #20276797 | C2 | semidirect |
| 6. #20276695 | C2 | semidirect |
| 7. #20276597 | C2 | semidirect |
| 8. C53×#2170 | C2 | semidirect |
| 142. #2170 | D53 | semidirect |
| 169. C53 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287868 | 2 |
| #20286520 | 2 |
| #20276968 | 2 |
| #20276840 | 2 |
| #20276797 | 2 |
| #20276695 | 2 |
| #20276597 | 2 |
| C53×#2170 | 2 |
| #33860 | 53 |