Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 26. #16810919 | C4 | semidirect |
| 27. #16810918 | C4 | semidirect |
| 28. #16810905 | C4 | semidirect |
| 32. C53×#475 | C4 | semidirect |
| 218. #475 | #6157 | semidirect |
| 236. C53 | #9178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291235 | 2 |
| #20290147 | 2 |
| #20290099 | 2 |
| #20290018 | 2 |
| #20289611 | 2 |
| #20289570 | 2 |
| #20284515 | 2 |
| #9178 | 53 |