Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #20276503 | C2 | semidirect |
| 4. #20275501 | C2 | semidirect |
| 5. #20272812 | C2 | semidirect |
| 6. #20272805 | C2 | semidirect |
| 25. C53×#361 | C4 | semidirect |
| 59. M32×C53 | C2×C4 | semidirect |
| 62. #108×C53 | C2×C4 | semidirect |
| 182. #361 | Dic53 | semidirect |
| 185. C53 | #12940 | semidirect |
| 205. M32 | C2×Dic53 | semidirect |
| 211. #108 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283567 | 2 |
| #20276503 | 2 |
| C2×#16810424 | 2 |
| #20275501 | 2 |
| #20272812 | 2 |
| #20272805 | 2 |
| C2×C53×#361 | 2 |
| #12940 | 53 |