Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
432 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20290816 | C2 | semidirect |
| 3. #20290284 | C2 | semidirect |
| 5. #20289613 | C2 | semidirect |
| 6. #20289554 | C2 | semidirect |
| 234. C53 | #8878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291443 | 2 |
| #20290816 | 2 |
| #20290284 | 2 |
| #20290020 | 2 |
| #20289613 | 2 |
| #20289554 | 2 |
| #20273208 | 2 |
| #8878 | 53 |