Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
954 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×#16810426 | C2 | semidirect |
| 3. C2×#16810423 | C2 | semidirect |
| 4. C2×C22⋊#11719908 | C2 | semidirect |
| 5. C53×#1808 | C2 | semidirect |
| 10. C2×#13133239 | C4 | semidirect |
| 97. Dic212 | C22⋊C4 | semidirect |
| 100. D424 | C22⋊C4 | semidirect |
| 166. #1808 | D53 | semidirect |
| 190. C53 | #12733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133239 | 2 |
| C2×#16810426 | 2 |
| C2×#16810423 | 2 |
| C2×C22⋊#11719908 | 2 |
| C53×#1808 | 2 |
| #12733 | 53 |