Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
248 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 3. #20289634 | C2 | semidirect |
| 4. #20289634 | C2 | semidirect |
| 5. #20289632 | C2 | semidirect |
| 6. #20289631 | C2 | semidirect |
| 70. C16×C53 | M16 | semidirect |
| 72. #11719908 | M16 | semidirect |
| 133. C53 | #11414 | semidirect |
| 181. C16 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291077 | 2 |
| #20289924 | 2 |
| #20289634 | 2 |
| #20289632 | 2 |
| #20289631 | 2 |
| M32×Dic53 | 2 |
| #11414 | 53 |