Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1854 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 1854 conjugacy classes of subgroups — too many to draw. Only its 272 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. C2×#16811567 | C2 | semidirect |
| 2. #20289905 | C2 | semidirect |
| 3. #20289898 | C2 | semidirect |
| 14. C2×#13133206 | C4 | semidirect |
| 15. C2×#13133205 | C4 | semidirect |
| 16. C2×#13133204 | C4 | semidirect |
| 17. C2×#13133203 | C4 | semidirect |
| 21. C2×#124×C53 | C4 | semidirect |
| 102. C42×C53 | C22⋊C4 | semidirect |
| 106. C4×Dic53 | C22⋊C4 | semidirect |
| 107. C4×Dic53 | C22⋊C4 | semidirect |
| 199. C2×#124 | #6157 | semidirect |
| 208. C53 | #14662 | semidirect |
| 294. C42 | C22⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811567 | 2 |
| #20289905 | 2 |
| #20289898 | 2 |
| #20289897 | 2 |
| C2×#124×D53 | 2 |
| #14662 | 53 |