Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
618 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 152 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. #20290630 | C2 | semidirect |
| 2. C42×#88324 | C2 | semidirect |
| 3. C2×Q8⋊#88324 | C2 | semidirect |
| 48. #124×C53 | C8 | semidirect |
| 173. C53 | #9639 | semidirect |
| 180. #124 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290630 | 2 |
| C42×#88324 | 2 |
| C2×Q8⋊#88324 | 2 |
| C2×D4⋊#88324 | 2 |
| #124×Dic53 | 2 |
| #9639 | 53 |