Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
636 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20287865 | C2 | semidirect |
| 2. #20286520 | C2 | semidirect |
| 3. #20276968 | C2 | semidirect |
| 4. #20276841 | C2 | semidirect |
| 5. #20276796 | C2 | semidirect |
| 6. #20276694 | C2 | semidirect |
| 7. #20276553 | C2 | semidirect |
| 8. C53×#2178 | C2 | semidirect |
| 141. #2178 | 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 |
|---|---|
| #20287865 | 2 |
| #20286520 | 2 |
| #20276968 | 2 |
| #20276841 | 2 |
| #20276796 | 2 |
| #20276694 | 2 |
| #20276553 | 2 |
| C53×#2178 | 2 |
| #33860 | 53 |