Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 98 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. #20290470 | C2 | semidirect |
| 4. #20289815 | C2 | semidirect |
| 9. #16811534 | C4 | semidirect |
| 10. #16811532 | C4 | semidirect |
| 14. C2×#13133223 | C4 | semidirect |
| 19. #16810647 | C4 | semidirect |
| 20. #16810589 | C4 | semidirect |
| 22. C2×C4×C8×C53 | C4 | semidirect |
| 168. C2×C4×C8 | #6157 | semidirect |
| 174. C53 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291008 | 2 |
| #20290988 | 2 |
| #20290470 | 2 |
| #20289815 | 2 |
| #20283428 | 2 |
| #12633 | 53 |