Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
812 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16810762 | C2 | semidirect |
| 3. #20275551 | C2 | semidirect |
| 4. #20274650 | C2 | semidirect |
| 5. #20273283 | C2 | semidirect |
| 6. #20272563 | C2 | semidirect |
| 7. C53×#2436 | C2 | semidirect |
| 236. #2436 | D53 | semidirect |
| 273. C53 | #9948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285463 | 2 |
| C2×#16810762 | 2 |
| #20275551 | 2 |
| #20274650 | 2 |
| #20273283 | 2 |
| #20272563 | 2 |
| C53×#2436 | 2 |
| #9948 | 53 |