Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
518 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 518 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 |
|---|---|---|
| 1. C22×#13133288 | C2 | semidirect |
| 2. C2×#16811537 | C2 | semidirect |
| 3. D53⋊(C22⋊C16) | C2 | semidirect |
| 4. #20289776 | C2 | semidirect |
| 35. #13133288 | D4 | semidirect |
| 169. C22×C53 | #359 | semidirect |
| 221. C53 | #12990 | semidirect |
| 374. C22 | #16811537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133288 | 2 |
| C2×#16811537 | 2 |
| D53⋊(C22⋊C16) | 2 |
| #20289776 | 2 |
| #20284294 | 2 |
| #12990 | 53 |