Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
846 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20284181 | C2 | semidirect |
| 2. C2×#16810736 | C2 | semidirect |
| 3. #20283434 | C2 | semidirect |
| 4. #20276162 | C2 | semidirect |
| 5. #20275825 | C2 | semidirect |
| 6. #20275222 | C2 | semidirect |
| 7. #20274704 | C2 | semidirect |
| 8. C53×#1838 | C2 | semidirect |
| 168. #1838 | D53 | semidirect |
| 196. C53 | #28177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284181 | 2 |
| C2×#16810736 | 2 |
| #20283434 | 2 |
| #20276162 | 2 |
| #20275825 | 2 |
| #20275222 | 2 |
| #20274704 | 2 |
| C53×#1838 | 2 |
| #28177 | 53 |