Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
582 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 118 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. #20290454 | C2 | semidirect |
| 4. #20289556 | C2 | semidirect |
| 6. C22×D53⋊C8 | C4 | semidirect |
| 10. C2×C4⋊#88324 | C4 | semidirect |
| 12. C2×#13133274 | C4 | semidirect |
| 15. C2×C4×#88324 | C4 | semidirect |
| 21. #16810349 | C4 | semidirect |
| 22. #16810346 | C4 | semidirect |
| 23. C53×#324 | C4 | semidirect |
| 109. C22×D53 | #97 | semidirect |
| 121. C2×C4×C53 | #97 | semidirect |
| 140. #88324 | #99 | semidirect |
| 195. #324 | #6157 | semidirect |
| 197. C53 | #8160 | semidirect |
| 308. C2×C4 | #13133271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811651 | 2 |
| #20290460 | 2 |
| #20290454 | 2 |
| #20289556 | 2 |
| #20273032 | 2 |
| #8160 | 53 |