Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
544 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #20285714 | C2 | semidirect |
| 3. #20273184 | C2 | semidirect |
| 4. #20273136 | C2 | semidirect |
| 5. #20273068 | C2 | semidirect |
| 6. #20272588 | C2 | semidirect |
| 7. C53×#3235 | C2 | semidirect |
| 196. #3235 | D53 | semidirect |
| 234. C53 | #10121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285714 | 2 |
| #20285183 | 2 |
| #20273184 | 2 |
| #20273136 | 2 |
| #20273068 | 2 |
| #20272588 | 2 |
| C53×#3235 | 2 |
| #10121 | 53 |