Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
326 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 326 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 |
|---|---|---|
| 1. D53⋊M64 | C2 | semidirect |
| 2. D53⋊#368 | C2 | semidirect |
| 3. #20289870 | C2 | semidirect |
| 6. #16811556 | C22 | semidirect |
| 9. #16811552 | C22 | semidirect |
| 120. D53 | #1419 | semidirect |
| 136. C53 | C2×#1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| D53⋊#368 | 2 |
| #20289870 | 2 |
| C2×D16×D53 | 2 |
| C2×#1419 | 53 |