Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
772 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20283760 | C2 | semidirect |
| 3. #20274636 | C2 | semidirect |
| 4. #20273256 | C2 | semidirect |
| 5. #20272621 | C2 | semidirect |
| 6. #20272592 | C2 | semidirect |
| 7. C53×#1786 | C2 | semidirect |
| 11. #16810774 | C4 | semidirect |
| 13. #16810757 | C4 | semidirect |
| 268. #1786 | D53 | semidirect |
| 307. C53 | #9520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283942 | 2 |
| #20283760 | 2 |
| #20274636 | 2 |
| #20273256 | 2 |
| #20272621 | 2 |
| #20272592 | 2 |
| C53×#1786 | 2 |
| #9520 | 53 |