Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
182 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 2. #20289879 | C2 | semidirect |
| 3. #20289878 | C2 | semidirect |
| 71. D53 | #1425 | semidirect |
| 82. C53 | C2×#1425 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#368 | 2 |
| #20289879 | 2 |
| #20289878 | 2 |
| C2×C32×D53 | 2 |
| C2×#1425 | 53 |