Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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. C4×#13133152 | C2 | semidirect |
| 3. #20273476 | C2 | semidirect |
| 6. #20272586 | C2 | semidirect |
| 7. C53×#1291 | C2 | semidirect |
| 168. #1291 | D53 | semidirect |
| 197. C53 | #8692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283684 | 2 |
| C4×#13133152 | 2 |
| #20273476 | 2 |
| #20273323 | 2 |
| #20273320 | 2 |
| #20272586 | 2 |
| C53×#1291 | 2 |
| #8692 | 53 |