Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 23. #16810372 | C4 | semidirect |
| 24. #16810370 | C4 | semidirect |
| 25. #16810368 | C4 | semidirect |
| 26. C53×#333 | C4 | semidirect |
| 172. #333 | #6157 | semidirect |
| 179. C53 | #9591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290890 | 2 |
| #20290830 | 2 |
| #20290065 | 2 |
| #20289927 | 2 |
| #20289612 | 2 |
| #20289549 | 2 |
| #20273369 | 2 |
| #9591 | 53 |