Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
184 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20277008 | C2 | semidirect |
| 3. #20272913 | C2 | semidirect |
| 4. #20272856 | C2 | semidirect |
| 5. C53×#1397 | C2 | semidirect |
| 65. #1397 | D53 | semidirect |
| 79. C53 | #13648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277008 | 2 |
| #20276553 | 2 |
| #20272913 | 2 |
| #20272856 | 2 |
| C53×#1397 | 2 |
| #13648 | 53 |