Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
184 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276990 | C2 | semidirect |
| 3. #20272897 | C2 | semidirect |
| 5. C53×#1397 | C2 | semidirect |
| 75. #1397 | D53 | semidirect |
| 89. C53 | #13722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276990 | 2 |
| #20276976 | 2 |
| #20272897 | 2 |
| #20272894 | 2 |
| C53×#1397 | 2 |
| #13722 | 53 |