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. #20283765 | C2 | semidirect |
| 3. #20274646 | C2 | semidirect |
| 4. #20273259 | C2 | semidirect |
| 5. #20272620 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 7. C53×#1783 | C2 | semidirect |
| 11. #16810774 | C4 | semidirect |
| 13. #16810757 | C4 | semidirect |
| 269. #1783 | 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 |
| #20283765 | 2 |
| #20274646 | 2 |
| #20273259 | 2 |
| #20272620 | 2 |
| #20272591 | 2 |
| C53×#1783 | 2 |
| #9520 | 53 |