Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
234 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 8. #16811511 | C4 | semidirect |
| 14. #16810399 | C4 | semidirect |
| 15. C53×#346 | C4 | semidirect |
| 104. #346 | #6157 | semidirect |
| 107. C53 | #7143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291078 | 2 |
| #20290428 | 2 |
| #20276516 | 2 |
| #7143 | 53 |