Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20295561 | C2 | semidirect |
| 2. #20295410 | C2 | semidirect |
| 3. #20295383 | C2 | semidirect |
| 4. #20295268 | C2 | semidirect |
| 6. #20295256 | C2 | semidirect |
| 7. #20295120 | C2 | semidirect |
| 8. #20295113 | C2 | semidirect |
| 9. #20295108 | C2 | semidirect |
| 10. C4×C8×D109 | C2 | semidirect |
| 11. #499×C109 | C2 | semidirect |
| 119. C109 | #3168 | semidirect |
| 121. #499 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295561 | 2 |
| #20295410 | 2 |
| #20295383 | 2 |
| #20295268 | 2 |
| #20295263 | 2 |
| #20295256 | 2 |
| #20295120 | 2 |
| #20295113 | 2 |
| #20295108 | 2 |
| C4×C8×D109 | 2 |
| #499×C109 | 2 |
| #3168 | 109 |