Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20289877 | C2 | semidirect |
| 3. #20289876 | C2 | semidirect |
| 9. C2×#13133123 | C4 | semidirect |
| 10. C32×D53 | C4 | semidirect |
| 11. C32×D53 | C4 | semidirect |
| 14. C2×C32×C53 | C4 | semidirect |
| 80. C2×C32 | #6157 | semidirect |
| 83. C53 | #13633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291066 | 2 |
| #20289877 | 2 |
| #20289876 | 2 |
| C2×C32×D53 | 2 |
| #13633 | 53 |