Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 387 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 |
|---|---|---|
| 7. #16810344 | C4 | semidirect |
| 8. C8×#88322 | C4 | semidirect |
| 21. C4×C8×C53 | C8 | semidirect |
| 71. C53 | #7841 | semidirect |
| 80. C4×C8 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274461 | 2 |
| C2×#16810344 | 2 |
| C2×C8×#88322 | 2 |
| C42×C8×C53 | 2 |
| #7841 | 53 |