Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
810 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 1. #20291444 | C2 | semidirect |
| 2. #20290853 | C2 | semidirect |
| 3. #20290706 | C2 | semidirect |
| 4. #20290640 | C2 | semidirect |
| 5. #20290433 | C2 | semidirect |
| 18. #16811006 | C4 | semidirect |
| 19. #16811003 | C4 | semidirect |
| 20. #16810995 | C4 | semidirect |
| 22. C53×#493 | C4 | semidirect |
| 125. #493 | #6157 | semidirect |
| 136. C53 | #22282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291444 | 2 |
| #20290853 | 2 |
| #20290706 | 2 |
| #20290640 | 2 |
| #20290433 | 2 |
| #20285142 | 2 |
| #22282 | 53 |