Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 126 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. #20289534 | C2 | semidirect |
| 4. #20289534 | C2 | semidirect |
| 32. #13133176 | C8 | semidirect |
| 92. C4⋊Dic53 | C2×C8 | semidirect |
| 93. C4⋊Dic53 | C2×C8 | semidirect |
| 208. C53 | #7579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290605 | 2 |
| C2×#16811489 | 2 |
| #20289534 | 2 |
| #20277197 | 2 |
| #7579 | 53 |