Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
526 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 14. #16811028 | C4 | semidirect |
| 16. #16811026 | C4 | semidirect |
| 19. C53×#500 | C4 | semidirect |
| 105. C8×C53 | #103 | semidirect |
| 106. #88322 | #103 | semidirect |
| 140. #500 | #6157 | semidirect |
| 150. C53 | #9823 | semidirect |
| 237. C8 | #13133280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290896 | 2 |
| #20290842 | 2 |
| #20290651 | 2 |
| C8×D53⋊C8 | 2 |
| #500×D53 | 2 |
| #9823 | 53 |