Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295560 | C2 | semidirect |
| 2. #20295432 | C2 | semidirect |
| 3. #20295413 | C2 | semidirect |
| 4. #20295390 | C2 | semidirect |
| 5. #20295388 | C2 | semidirect |
| 6. #20295277 | C2 | semidirect |
| 7. #20295270 | C2 | semidirect |
| 8. C4×#13182017 | C2 | semidirect |
| 9. C4×#13182014 | C2 | semidirect |
| 10. C4×#13182013 | C2 | semidirect |
| 11. #532×C109 | C2 | semidirect |
| 110. #11724784 | #41 | semidirect |
| 138. C109 | #3171 | semidirect |
| 139. #532 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295560 | 2 |
| #20295432 | 2 |
| #20295413 | 2 |
| #20295390 | 2 |
| #20295388 | 2 |
| #20295277 | 2 |
| #20295270 | 2 |
| C4×#13182017 | 2 |
| C4×#13182014 | 2 |
| C4×#13182013 | 2 |
| #532×C109 | 2 |
| #3171 | 109 |