Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
950 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20274711 | C2 | semidirect |
| 3. #20273390 | C2 | semidirect |
| 4. #20273167 | C2 | semidirect |
| 5. C53×#1984 | C2 | semidirect |
| 169. #1984 | D53 | semidirect |
| 197. C53 | #8354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288486 | 2 |
| #20274711 | 2 |
| #20273390 | 2 |
| #20273167 | 2 |
| C53×#1984 | 2 |
| #8354 | 53 |