Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 96 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. #20291066 | C2 | semidirect |
| 3. #20289783 | C2 | semidirect |
| 13. C2×#13133157 | C4 | semidirect |
| 14. C2×#13133156 | C4 | semidirect |
| 16. C2×C16×D53 | C4 | semidirect |
| 18. C22×C16×C53 | C4 | semidirect |
| 130. C22×C16 | #6157 | semidirect |
| 136. C53 | #12839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291066 | 2 |
| #20290597 | 2 |
| #20289783 | 2 |
| C2×#16811039 | 2 |
| #12839 | 53 |