Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4614 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 4614 conjugacy classes of subgroups — too many to draw. Only its 491 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. C2×#16810470 | C2 | semidirect |
| 3. #20272986 | C2 | semidirect |
| 4. #20272955 | C2 | semidirect |
| 5. C53×#1446 | C2 | semidirect |
| 7. C22×#11719949 | C4 | semidirect |
| 50. C22×C4×C53 | #41 | semidirect |
| 55. C22×Dic53 | #41 | semidirect |
| 62. C2×C4×D53 | C22⋊C4 | semidirect |
| 112. #1446 | D53 | semidirect |
| 129. C53 | #13851 | semidirect |
| 176. C22×C4 | #11719949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719949 | 2 |
| C2×#16810470 | 2 |
| #20272986 | 2 |
| #20272955 | 2 |
| C53×#1446 | 2 |
| #13851 | 53 |