Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1214 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1214 conjugacy classes of subgroups — too many to draw. Only its 191 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. #20285111 | C2 | semidirect |
| 3. #20275944 | C2 | semidirect |
| 4. #20275633 | C2 | semidirect |
| 5. #20274673 | C2 | semidirect |
| 6. C4×#13133136 | C2 | semidirect |
| 7. C53×#2568 | C2 | semidirect |
| 182. #2568 | D53 | semidirect |
| 216. C53 | #25872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20285111 | 2 |
| #20275944 | 2 |
| #20275633 | 2 |
| #20274673 | 2 |
| C4×#13133136 | 2 |
| C53×#2568 | 2 |
| #25872 | 53 |