Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 19. C2×#11719917 | C8 | semidirect |
| 29. C2×M16×C53 | C8 | semidirect |
| 137. C53 | #7026 | semidirect |
| 148. C2×M16 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊#88324 | 2 |
| #20274408 | 2 |
| #7026 | 53 |