Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20272789 | C2 | semidirect |
| 4. #20272787 | C2 | semidirect |
| 53. C16×C53 | M16 | semidirect |
| 107. C53 | #12025 | semidirect |
| 143. C16 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273478 | 2 |
| #20273474 | 2 |
| #20272789 | 2 |
| #20272787 | 2 |
| C4×M32×C53 | 2 |
| #12025 | 53 |