Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
242 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 2. #20289749 | C2 | semidirect |
| 3. #20289748 | C2 | semidirect |
| 48. C16×C53 | M16 | semidirect |
| 50. #11719908 | M16 | semidirect |
| 98. C53 | #12023 | semidirect |
| 134. C16 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290272 | 2 |
| #20289749 | 2 |
| #20289748 | 2 |
| C2×C16×Dic53 | 2 |
| #12023 | 53 |