Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
480 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20276298 | C2 | semidirect |
| 2. #20276167 | C2 | semidirect |
| 4. #20275420 | C2 | semidirect |
| 6. #20274956 | C2 | semidirect |
| 7. #20274933 | C2 | semidirect |
| 8. #20274852 | C2 | semidirect |
| 9. C53×#2102 | C2 | semidirect |
| 137. #2102 | D53 | semidirect |
| 170. C53 | #32702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276298 | 2 |
| #20276167 | 2 |
| #20276002 | 2 |
| #20275420 | 2 |
| #20275076 | 2 |
| #20274956 | 2 |
| #20274933 | 2 |
| #20274852 | 2 |
| C53×#2102 | 2 |
| #32702 | 53 |