Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20275703 | C2 | semidirect |
| 4. #20273397 | C2 | semidirect |
| 6. C8×#11719917 | C2 | semidirect |
| 7. C53×#1566 | C2 | semidirect |
| 95. #11719917 | SD16 | semidirect |
| 129. C8×C53 | #100 | semidirect |
| 152. #1566 | D53 | semidirect |
| 179. C53 | #9793 | semidirect |
| 285. C8 | #13133133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810996 | 2 |
| #20275703 | 2 |
| #20275554 | 2 |
| #20273397 | 2 |
| #20273384 | 2 |
| C8×#11719917 | 2 |
| C53×#1566 | 2 |
| #9793 | 53 |