Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20274783 | C2 | semidirect |
| 3. #20272540 | C2 | semidirect |
| 4. #20272535 | C2 | semidirect |
| 5. C4×C22⋊C8×C53 | C2 | semidirect |
| 186. C4×C22⋊C8 | D53 | semidirect |
| 215. C53 | #7670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283016 | 2 |
| #20274783 | 2 |
| #20272540 | 2 |
| #20272535 | 2 |
| C4×C22⋊C8×C53 | 2 |
| #7670 | 53 |