Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20273008 | C2 | semidirect |
| 4. #20272560 | C2 | semidirect |
| 5. C53×#1281 | C2 | semidirect |
| 141. #1281 | D53 | semidirect |
| 162. C53 | #8157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810580 | 2 |
| #20273027 | 2 |
| #20273008 | 2 |
| #20272560 | 2 |
| C53×#1281 | 2 |
| #8157 | 53 |