Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
164 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 27 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. #20272882 | C2 | semidirect |
| 2. #20272880 | C2 | semidirect |
| 7. C53×#493 | C4 | semidirect |
| 10. C53×#322 | C4 | semidirect |
| 71. #493 | Dic53 | semidirect |
| 76. #322 | Dic53 | semidirect |
| 77. C53 | #7527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272882 | 2 |
| #20272880 | 2 |
| C53×#1721 | 2 |
| #7527 | 53 |