Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16810349 | C2 | semidirect |
| 3. #20272741 | C2 | semidirect |
| 4. #20272717 | C2 | semidirect |
| 5. C53×#1821 | C2 | semidirect |
| 179. #1821 | D53 | semidirect |
| 208. C53 | #11852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280195 | 2 |
| C2×#16810349 | 2 |
| #20272741 | 2 |
| #20272717 | 2 |
| C53×#1821 | 2 |
| #11852 | 53 |