Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
932 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 114 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. C2×#16811537 | C2 | semidirect |
| 2. D53⋊(C22⋊C16) | C2 | semidirect |
| 3. #20290595 | C2 | semidirect |
| 5. C2×D53⋊C16 | C22 | semidirect |
| 6. C2×#13133288 | C22 | semidirect |
| 161. C22×C53 | #359 | semidirect |
| 204. C53 | #12734 | semidirect |
| 350. C22 | #16811537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811537 | 2 |
| D53⋊(C22⋊C16) | 2 |
| #20290595 | 2 |
| C22×#13133236 | 2 |
| #12734 | 53 |