Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
426 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20283816 | C2 | semidirect |
| 3. #20273309 | C2 | semidirect |
| 6. #20272552 | C2 | semidirect |
| 7. C53×#1278 | C2 | semidirect |
| 181. #1278 | D53 | semidirect |
| 210. C53 | #9070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285038 | 2 |
| #20283816 | 2 |
| #20273309 | 2 |
| #20273133 | 2 |
| #20273131 | 2 |
| #20272552 | 2 |
| C53×#1278 | 2 |
| #9070 | 53 |