Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20275551 | C2 | semidirect |
| 3. #20275144 | C2 | semidirect |
| 4. #20275141 | C2 | semidirect |
| 5. #20274895 | C2 | semidirect |
| 6. #20272582 | C2 | semidirect |
| 7. C53×#1964 | C2 | semidirect |
| 129. C22⋊C4×C53 | D8 | semidirect |
| 261. #1964 | D53 | semidirect |
| 300. C53 | #10564 | semidirect |
| 420. C22⋊C4 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285463 | 2 |
| #20275551 | 2 |
| #20275144 | 2 |
| #20275141 | 2 |
| #20274895 | 2 |
| #20272582 | 2 |
| C53×#1964 | 2 |
| #10564 | 53 |