Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
652 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20275693 | C2 | semidirect |
| 4. #20273396 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#3209 | C2 | semidirect |
| 174. #3209 | D53 | semidirect |
| 207. C53 | #10291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285653 | 2 |
| #20283073 | 2 |
| #20275693 | 2 |
| #20273396 | 2 |
| #20273382 | 2 |
| #20272547 | 2 |
| C53×#3209 | 2 |
| #10291 | 53 |