Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
294 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 98 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. D53⋊M64 | C2 | semidirect |
| 2. C2×D53⋊C32 | C2 | semidirect |
| 3. #20289833 | C2 | semidirect |
| 4. #20289832 | C2 | semidirect |
| 7. #16811555 | C22 | semidirect |
| 11. C2×#13133267 | C22 | semidirect |
| 142. D53 | #1401 | semidirect |
| 160. C53 | C2×#1401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| C2×D53⋊C32 | 2 |
| #20289833 | 2 |
| #20289832 | 2 |
| #504×D53 | 2 |
| C2×#1401 | 53 |