Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20283805 | C2 | semidirect |
| 4. #20273161 | C2 | semidirect |
| 6. #20272565 | C2 | semidirect |
| 7. C53×#1290 | C2 | semidirect |
| 209. #1290 | D53 | semidirect |
| 242. C53 | #9244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810846 | 2 |
| #20283805 | 2 |
| #20273314 | 2 |
| #20273161 | 2 |
| #20273068 | 2 |
| #20272565 | 2 |
| C53×#1290 | 2 |
| #9244 | 53 |