Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20283777 | C2 | semidirect |
| 2. #20273271 | C2 | semidirect |
| 3. #20273244 | C2 | semidirect |
| 4. #20273075 | C2 | semidirect |
| 5. #20272624 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 26. C53×#483 | C4 | semidirect |
| 28. C53×#480 | C4 | semidirect |
| 31. C53×#450 | C4 | semidirect |
| 33. C53×#447 | C4 | semidirect |
| 235. #483 | Dic53 | semidirect |
| 237. #480 | Dic53 | semidirect |
| 240. #450 | Dic53 | semidirect |
| 242. #447 | Dic53 | semidirect |
| 260. C53 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283777 | 2 |
| #20273271 | 2 |
| #20273244 | 2 |
| #20273075 | 2 |
| #20272624 | 2 |
| #20272591 | 2 |
| C53×#3194 | 2 |
| #9332 | 53 |