Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20274851 | C2 | semidirect |
| 4. #20272733 | C2 | semidirect |
| 7. C53×#1350 | C2 | semidirect |
| 149. #1350 | D53 | semidirect |
| 176. C53 | #11866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285286 | 2 |
| #20276515 | 2 |
| #20274851 | 2 |
| #20272733 | 2 |
| #20272731 | 2 |
| #20272729 | 2 |
| C53×#1350 | 2 |
| #11866 | 53 |