Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
934 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 183 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. #20273757 | C2 | semidirect |
| 5. #20273227 | C2 | semidirect |
| 6. #20273059 | C2 | semidirect |
| 7. C53×#3502 | C2 | semidirect |
| 178. #3502 | D53 | semidirect |
| 214. C53 | #18188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284810 | 2 |
| #20277998 | 2 |
| #20273757 | 2 |
| #20273655 | 2 |
| #20273227 | 2 |
| #20273059 | 2 |
| C53×#3502 | 2 |
| #18188 | 53 |