Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20276326 | C2 | semidirect |
| 3. #20272732 | C2 | semidirect |
| 4. #20272729 | C2 | semidirect |
| 5. C53×#1810 | C2 | semidirect |
| 163. #1810 | D53 | semidirect |
| 190. C53 | #11894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284296 | 2 |
| #20276326 | 2 |
| #20272732 | 2 |
| #20272729 | 2 |
| C53×#1810 | 2 |
| #11894 | 53 |