Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20273478 | C2 | semidirect |
| 4. #20272571 | C2 | semidirect |
| 5. C4×#106×C53 | C2 | semidirect |
| 7. #16810753 | C4 | semidirect |
| 8. C8×Dic106 | C4 | semidirect |
| 9. #16810702 | C4 | semidirect |
| 11. C8×D212 | C4 | semidirect |
| 149. C4×#106 | D53 | semidirect |
| 177. C53 | #8696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283690 | 2 |
| #20273478 | 2 |
| #20273238 | 2 |
| #20272571 | 2 |
| C4×#106×C53 | 2 |
| #8696 | 53 |