Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20274895 | C2 | semidirect |
| 4. #20272563 | C2 | semidirect |
| 80. C22⋊C4×C53 | M16 | semidirect |
| 198. C53 | #8852 | semidirect |
| 271. C22⋊C4 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283744 | 2 |
| #20275008 | 2 |
| #20274895 | 2 |
| #20272563 | 2 |
| C4×#99×C53 | 2 |
| #8852 | 53 |