Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #20274463 | C2 | semidirect |
| 4. #20272597 | C2 | semidirect |
| 17. #16810363 | C4 | semidirect |
| 20. C53×#329 | C4 | semidirect |
| 36. #13133128 | C2×C4 | semidirect |
| 48. #97×C53 | C2×C4 | semidirect |
| 170. #329 | Dic53 | semidirect |
| 171. C53 | #8224 | semidirect |
| 197. #97 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×Dic53 | 2 |
| #20274463 | 2 |
| C2×#16810363 | 2 |
| #20272597 | 2 |
| C2×C53×#329 | 2 |
| #8224 | 53 |