Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
134 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 134 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. #20289885 | C2 | semidirect |
| 2. #20289884 | C2 | semidirect |
| 3. D53⋊C64 | C2 | semidirect |
| 5. #16811462 | C22 | semidirect |
| 62. D53 | M128 | semidirect |
| 71. C53 | C2×M128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289885 | 2 |
| #20289884 | 2 |
| D53⋊C64 | 2 |
| C2×C32×D53 | 2 |
| C2×M128 | 53 |