Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #20283583 | C2 | semidirect |
| 4. #20276779 | C2 | semidirect |
| 5. #20276763 | C2 | semidirect |
| 6. #20276473 | C2 | semidirect |
| 7. #20276435 | C2 | semidirect |
| 9. C22×Q32×C53 | C2 | semidirect |
| 169. C22×Q32 | D53 | semidirect |
| 206. C53 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811064 | 2 |
| #20285204 | 2 |
| #20283583 | 2 |
| #20276779 | 2 |
| #20276763 | 2 |
| #20276473 | 2 |
| #20276435 | 2 |
| #20276423 | 2 |
| C22×Q32×C53 | 2 |
| #33588 | 53 |