Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
884 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 146 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. #20290569 | C2 | semidirect |
| 2. C4×C22⋊#88324 | C2 | semidirect |
| 3. #20289532 | C2 | semidirect |
| 9. #16811489 | C22 | semidirect |
| 10. #16811489 | C22 | semidirect |
| 31. C22×D212 | C8 | semidirect |
| 224. C53 | #7572 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290569 | 2 |
| C4×C22⋊#88324 | 2 |
| #20289532 | 2 |
| C2×#16810524 | 2 |
| #7572 | 53 |