Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
152 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20272787 | C2 | semidirect |
| 3. C53×C4⋊C32 | C2 | semidirect |
| 58. C4⋊C32 | D53 | semidirect |
| 70. C53 | #7444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276965 | 2 |
| #20272787 | 2 |
| C53×C4⋊C32 | 2 |
| #7444 | 53 |