Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1218 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1218 conjugacy classes of subgroups — too many to draw. Only its 219 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×#13133209 | C2 | semidirect |
| 2. C2×#16810988 | C2 | semidirect |
| 4. #20275862 | C2 | semidirect |
| 5. #20275684 | C2 | semidirect |
| 6. #20275030 | C2 | semidirect |
| 7. C53×#1749 | C2 | semidirect |
| 35. #13133209 | D4 | semidirect |
| 138. C22×C53 | #490 | semidirect |
| 161. #1749 | D53 | semidirect |
| 188. C53 | #25913 | semidirect |
| 304. C22 | #16810988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133209 | 2 |
| C2×#16810988 | 2 |
| #20283060 | 2 |
| #20275862 | 2 |
| #20275684 | 2 |
| #20275030 | 2 |
| C53×#1749 | 2 |
| #25913 | 53 |