Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 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 |
|---|---|---|
| 1. C2×#16811039 | C2 | semidirect |
| 2. #20284359 | C2 | semidirect |
| 3. #20276815 | C2 | semidirect |
| 4. #20276798 | C2 | semidirect |
| 5. #20276499 | C2 | semidirect |
| 6. #20276431 | C2 | semidirect |
| 7. C22×D16×C53 | C2 | semidirect |
| 12. C2×#13133156 | C22 | semidirect |
| 13. C2×C16×D53 | C22 | semidirect |
| 15. #16810856 | C22 | semidirect |
| 18. #16810451 | C22 | semidirect |
| 19. #16810449 | C22 | semidirect |
| 20. #16810424 | C22 | semidirect |
| 52. C2×C16×C53 | D4 | semidirect |
| 125. C22×D16 | D53 | semidirect |
| 155. C53 | #33607 | semidirect |
| 179. C2×C16 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811039 | 2 |
| #20284359 | 2 |
| #20276815 | 2 |
| #20276798 | 2 |
| #20276499 | 2 |
| #20276431 | 2 |
| C22×D16×C53 | 2 |
| #33607 | 53 |