Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C4⋊#88322 | C2 | semidirect |
| 2. #20273487 | C2 | semidirect |
| 5. #20272610 | C2 | semidirect |
| 6. #20272548 | C2 | semidirect |
| 15. #16810369 | C4 | semidirect |
| 16. #16810367 | C4 | semidirect |
| 178. C53 | #9578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#88322 | 2 |
| #20273487 | 2 |
| #20273364 | 2 |
| #20273114 | 2 |
| #20272610 | 2 |
| #20272548 | 2 |
| C53×#1962 | 2 |
| #9578 | 53 |