Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
548 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20277688 | C2 | semidirect |
| 3. #20273276 | C2 | semidirect |
| 4. #20273211 | C2 | semidirect |
| 5. #20272617 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#1478 | C2 | semidirect |
| 11. #16810828 | C4 | semidirect |
| 12. #16810818 | C4 | semidirect |
| 207. #1478 | D53 | semidirect |
| 238. C53 | #9181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284179 | 2 |
| #20277688 | 2 |
| #20273276 | 2 |
| #20273211 | 2 |
| #20272617 | 2 |
| #20272574 | 2 |
| C53×#1478 | 2 |
| #9181 | 53 |