Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276464 | C2 | semidirect |
| 3. C2×#16810437 | C2 | semidirect |
| 4. C2×#16810435 | C2 | semidirect |
| 5. #20275506 | C2 | semidirect |
| 6. #20272802 | C2 | semidirect |
| 7. C53×#2143 | C2 | semidirect |
| 67. #108×C53 | D4 | semidirect |
| 173. #2143 | D53 | semidirect |
| 201. C53 | #13417 | semidirect |
| 240. #108 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285202 | 2 |
| #20276464 | 2 |
| C2×#16810437 | 2 |
| C2×#16810435 | 2 |
| #20275506 | 2 |
| #20272802 | 2 |
| C53×#2143 | 2 |
| #13417 | 53 |