Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
622 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 622 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. C2×#16810349 | C2 | semidirect |
| 4. #20272582 | C2 | semidirect |
| 5. C53×#2316 | C2 | semidirect |
| 9. #16810553 | C4 | semidirect |
| 11. #16810540 | C4 | semidirect |
| 179. #2316 | D53 | semidirect |
| 208. C53 | #9204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280457 | 2 |
| #20273282 | 2 |
| C2×#16810349 | 2 |
| #20272582 | 2 |
| C53×#2316 | 2 |
| #9204 | 53 |