Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 92 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. C2×D53⋊C32 | C2 | semidirect |
| 2. C22×#13133267 | C2 | semidirect |
| 3. #20289873 | C2 | semidirect |
| 4. #20289829 | C2 | semidirect |
| 5. C22⋊#13133267 | C2 | semidirect |
| 6. #20289820 | C2 | semidirect |
| 24. #13133267 | D4 | semidirect |
| 66. C22⋊D53 | C32 | semidirect |
| 80. C22×C53 | C2×C32 | semidirect |
| 84. C2×D53 | C2×C32 | semidirect |
| 90. Dic53 | C2×C32 | semidirect |
| 116. C53 | D4×C32 | semidirect |
| 178. C22 | D53⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊C32 | 2 |
| C22×#13133267 | 2 |
| #20289873 | 2 |
| #20289829 | 2 |
| C22⋊#13133267 | 2 |
| #20289820 | 2 |
| #20276532 | 2 |
| D4×C32 | 53 |