Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 3. #20273266 | C2 | semidirect |
| 4. #20273136 | C2 | semidirect |
| 5. #20272581 | C2 | semidirect |
| 6. #20272576 | C2 | semidirect |
| 26. C53×#501 | C4 | semidirect |
| 27. C53×#501 | C4 | semidirect |
| 28. C53×#489 | C4 | semidirect |
| 29. C53×#489 | C4 | semidirect |
| 199. #501 | Dic53 | semidirect |
| 200. #501 | Dic53 | semidirect |
| 201. #489 | Dic53 | semidirect |
| 202. #489 | Dic53 | semidirect |
| 224. C53 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283702 | 2 |
| #20273292 | 2 |
| #20273266 | 2 |
| #20273136 | 2 |
| #20272581 | 2 |
| #20272576 | 2 |
| C53×#3240 | 2 |
| #9369 | 53 |