Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
610 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 128 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. #20290648 | C2 | semidirect |
| 2. C4×#13133272 | C2 | semidirect |
| 3. C2×Q8⋊#88324 | C2 | semidirect |
| 179. C53 | #9646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290648 | 2 |
| C4×#13133272 | 2 |
| C2×Q8⋊#88324 | 2 |
| C2×D4⋊#88324 | 2 |
| #124×Dic53 | 2 |
| #9646 | 53 |