Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #20274868 | C2 | semidirect |
| 3. #20273491 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 7. C53×#1571 | C2 | semidirect |
| 128. #1571 | D53 | semidirect |
| 150. C53 | #10667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275546 | 2 |
| #20274868 | 2 |
| #20273491 | 2 |
| #20273115 | 2 |
| #20273113 | 2 |
| #20272543 | 2 |
| C53×#1571 | 2 |
| #10667 | 53 |