Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20275689 | C2 | semidirect |
| 4. #20272597 | C2 | semidirect |
| 20. C53×#497 | C4 | semidirect |
| 47. C4⋊Q8×C53 | C2×C4 | semidirect |
| 55. #97×C53 | C2×C4 | semidirect |
| 172. #497 | Dic53 | semidirect |
| 183. C53 | #9003 | semidirect |
| 198. C4⋊Q8 | C2×Dic53 | semidirect |
| 214. #97 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277889 | 2 |
| #20275689 | 2 |
| C2×#16810363 | 2 |
| #20272597 | 2 |
| C2×C53×#497 | 2 |
| #9003 | 53 |