Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
192 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 6. #16810401 | C4 | semidirect |
| 14. C53×#322 | C4 | semidirect |
| 15. C82×C53 | C4 | semidirect |
| 93. #322 | Dic53 | semidirect |
| 94. C82 | Dic53 | semidirect |
| 95. C53 | #7225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276527 | 2 |
| #20274864 | 2 |
| C53×#1455 | 2 |
| #7225 | 53 |