Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
884 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#16811000 | C2 | semidirect |
| 2. #20284195 | C2 | semidirect |
| 3. #20275971 | C2 | semidirect |
| 4. #20275824 | C2 | semidirect |
| 5. #20275555 | C2 | semidirect |
| 6. #20274853 | C2 | semidirect |
| 7. C53×#2922 | C2 | semidirect |
| 133. #2922 | D53 | semidirect |
| 161. C53 | #29818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| #20284195 | 2 |
| #20275971 | 2 |
| #20275824 | 2 |
| #20275555 | 2 |
| #20274853 | 2 |
| C53×#2922 | 2 |
| #29818 | 53 |