Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
682 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20275656 | C2 | semidirect |
| 3. #20273416 | C2 | semidirect |
| 5. #20273331 | C2 | semidirect |
| 7. C53×#1467 | C2 | semidirect |
| 206. #1467 | D53 | semidirect |
| 237. C53 | #8461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288580 | 2 |
| #20275656 | 2 |
| #20273416 | 2 |
| #20273411 | 2 |
| #20273331 | 2 |
| #20273327 | 2 |
| C53×#1467 | 2 |
| #8461 | 53 |