Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20272598 | C2 | semidirect |
| 4. #20272556 | C2 | semidirect |
| 5. C53×#2571 | C2 | semidirect |
| 127. #2571 | D53 | semidirect |
| 149. C53 | #10351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275642 | 2 |
| #20275520 | 2 |
| #20272598 | 2 |
| #20272556 | 2 |
| C53×#2571 | 2 |
| #10351 | 53 |