Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
908 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20274649 | C2 | semidirect |
| 4. #20272593 | C2 | semidirect |
| 11. #16810535 | C4 | semidirect |
| 24. C22×Dic106 | C2×C4 | semidirect |
| 35. #13133124 | C2×C4 | semidirect |
| 120. C23×C53 | #103 | semidirect |
| 218. C53 | #9013 | semidirect |
| 319. C23 | #13133140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810535 | 2 |
| #20274649 | 2 |
| C2×#16810347 | 2 |
| #20272593 | 2 |
| C53×#2315 | 2 |
| #9013 | 53 |