Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
226 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #20272781 | C2 | semidirect |
| 5. #20272780 | C2 | semidirect |
| 6. #20272780 | C2 | semidirect |
| 7. C53×#1368 | C2 | semidirect |
| 64. C16×C53 | M16 | semidirect |
| 66. #11719908 | M16 | semidirect |
| 105. #1368 | D53 | semidirect |
| 125. C53 | #12019 | semidirect |
| 169. C16 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #346×D53 | 2 |
| #20273475 | 2 |
| #20273469 | 2 |
| #20272781 | 2 |
| #20272780 | 2 |
| C53×#1368 | 2 |
| #12019 | 53 |