Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20276515 | C2 | semidirect |
| 3. #20276511 | C2 | semidirect |
| 4. #20272641 | C2 | semidirect |
| 5. #20272640 | C2 | semidirect |
| 6. #20272640 | C2 | semidirect |
| 7. C53×#1315 | C2 | semidirect |
| 166. #1315 | D53 | semidirect |
| 192. C53 | #11492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283423 | 2 |
| #20276515 | 2 |
| #20276511 | 2 |
| #20272641 | 2 |
| #20272640 | 2 |
| C53×#1315 | 2 |
| #11492 | 53 |