Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20275544 | C2 | semidirect |
| 2. #20274460 | C2 | semidirect |
| 3. #20273474 | C2 | semidirect |
| 4. #20273166 | C2 | semidirect |
| 14. C53×#500 | C4 | semidirect |
| 15. C53×#493 | C4 | semidirect |
| 16. C53×#486 | C4 | semidirect |
| 73. C4×Dic53 | D8 | semidirect |
| 133. #500 | Dic53 | semidirect |
| 134. #493 | Dic53 | semidirect |
| 135. #486 | Dic53 | semidirect |
| 146. C53 | #9847 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275544 | 2 |
| #20274460 | 2 |
| #20273474 | 2 |
| #20273166 | 2 |
| C53×#3169 | 2 |
| #9847 | 53 |