Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
504 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 504 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. C2×#16810405 | C2 | semidirect |
| 3. #20272650 | C2 | semidirect |
| 4. C2×C53×#349 | C2 | semidirect |
| 183. C2×#349 | D53 | semidirect |
| 207. C53 | #11436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283159 | 2 |
| C2×#16810405 | 2 |
| #20272650 | 2 |
| C2×C53×#349 | 2 |
| #11436 | 53 |