Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
196 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 51 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. #20276966 | C2 | semidirect |
| 5. #20272912 | C2 | semidirect |
| 6. #20272907 | C2 | semidirect |
| 7. C53×#1420 | C2 | semidirect |
| 98. #1420 | D53 | semidirect |
| 117. C53 | #13693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277035 | 2 |
| #20277033 | 2 |
| #20276966 | 2 |
| #20276595 | 2 |
| #20272912 | 2 |
| #20272907 | 2 |
| C53×#1420 | 2 |
| #13693 | 53 |