Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #20275560 | C2 | semidirect |
| 4. #20273310 | C2 | semidirect |
| 6. #20272606 | C2 | semidirect |
| 7. C53×#3230 | C2 | semidirect |
| 176. #3230 | D53 | semidirect |
| 210. C53 | #10109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286098 | 2 |
| #20285111 | 2 |
| #20275560 | 2 |
| #20273310 | 2 |
| #20273131 | 2 |
| #20272606 | 2 |
| C53×#3230 | 2 |
| #10109 | 53 |