Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
650 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20277076 | C2 | semidirect |
| 2. #20275635 | C2 | semidirect |
| 3. #20273223 | C2 | semidirect |
| 4. #20273158 | C2 | semidirect |
| 5. #20272607 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 24. C53×#476 | C4 | semidirect |
| 25. C53×#459 | C4 | semidirect |
| 52. C4⋊Q8×C53 | C2×C4 | semidirect |
| 53. #127×C53 | C2×C4 | semidirect |
| 67. C4⋊C8×C53 | C2×C4 | semidirect |
| 135. D4×C53 | #104 | semidirect |
| 208. #476 | Dic53 | semidirect |
| 209. #459 | Dic53 | semidirect |
| 225. C53 | #9325 | semidirect |
| 232. C4⋊Q8 | C2×Dic53 | semidirect |
| 233. #127 | C2×Dic53 | semidirect |
| 254. C4⋊C8 | C2×Dic53 | semidirect |
| 332. D4 | #13133144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277076 | 2 |
| #20275635 | 2 |
| #20273223 | 2 |
| #20273158 | 2 |
| #20272607 | 2 |
| #20272572 | 2 |
| C53×#3109 | 2 |
| #9325 | 53 |