Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 294 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. C4×#88322 | C8 | semidirect |
| 23. C4×C8×C53 | C8 | semidirect |
| 101. C53 | #7018 | semidirect |
| 115. C4×C8 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290630 | 2 |
| #20274460 | 2 |
| #7018 | 53 |