Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
702 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#16810419 | C2 | semidirect |
| 3. #20274639 | C2 | semidirect |
| 4. #20272841 | C2 | semidirect |
| 5. C22×#101×C53 | C2 | semidirect |
| 71. #101×C53 | D4 | semidirect |
| 206. C22×C53 | #355 | semidirect |
| 225. C22×#101 | D53 | semidirect |
| 257. C53 | #13092 | semidirect |
| 297. #101 | C22⋊D53 | semidirect |
| 443. C22 | #16810419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278369 | 2 |
| C2×#16810419 | 2 |
| #20274639 | 2 |
| #20272841 | 2 |
| C22×#101×C53 | 2 |
| #13092 | 53 |