Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
584 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20276117 | C2 | semidirect |
| 4. #20276116 | C2 | semidirect |
| 5. #20276115 | C2 | semidirect |
| 7. C53×#2070 | C2 | semidirect |
| 105. #2070 | D53 | semidirect |
| 123. C53 | #32876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276232 | 2 |
| #20276230 | 2 |
| #20276117 | 2 |
| #20276116 | 2 |
| #20276115 | 2 |
| #20274637 | 2 |
| C53×#2070 | 2 |
| #32876 | 53 |