Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 13. C8×#88324 | C4 | semidirect |
| 14. C8×#88324 | C4 | semidirect |
| 17. #16810374 | C4 | semidirect |
| 18. #16810373 | C4 | semidirect |
| 19. C53×#334 | C4 | semidirect |
| 25. #13133285 | C8 | semidirect |
| 88. #88324 | #106 | semidirect |
| 91. C8×C53 | C4×C8 | semidirect |
| 94. #88322 | C4×C8 | semidirect |
| 129. #334 | #6157 | semidirect |
| 132. C53 | C8×#106 | semidirect |
| 207. C8 | C8×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133285 | 2 |
| #20290508 | 2 |
| C8×D53⋊C8 | 2 |
| #20289549 | 2 |
| #334×D53 | 2 |
| C8×#106 | 53 |