Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3590 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 3590 conjugacy classes of subgroups — too many to draw. Only its 907 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. C22×#13133217 | C2 | semidirect |
| 3. #20280825 | C2 | direct (N × H) |
| 4. C2×#16810560 | C2 | semidirect |
| 5. C2×C53×#376 | C2 | semidirect |
| 9. C2×#13133217 | C22 | semidirect |
| 14. #16810560 | C22 | semidirect |
| 16. C53×#376 | C22 | semidirect |
| 88. C2×#376 | D53 | semidirect |
| 89. C2×C53 | #2658 | semidirect |
| 103. #376 | C2×D53 | semidirect |
| 105. C53 | C2×#2658 | semidirect |
| 172. C2 | #20280825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133217 | 2 |
| C22×#13133205 | 2 |
| #20280825 | 2 |
| C2×#16810560 | 2 |
| C2×C53×#376 | 2 |
| C2×#2658 | 53 |