Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20275705 | C2 | semidirect |
| 3. #20273471 | C2 | semidirect |
| 4. #20273396 | C2 | semidirect |
| 6. C8×#11719917 | C2 | semidirect |
| 95. #11719917 | SD16 | semidirect |
| 127. C8×C53 | #100 | semidirect |
| 179. C53 | #9793 | semidirect |
| 285. C8 | #13133134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275705 | 2 |
| #20275556 | 2 |
| #20273471 | 2 |
| #20273396 | 2 |
| #20273383 | 2 |
| C8×#11719917 | 2 |
| C2×C53×#492 | 2 |
| #9793 | 53 |