Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20295729 | C2 | semidirect |
| 2. #20295353 | C2 | semidirect |
| 3. #20295341 | C2 | semidirect |
| 4. #20295323 | C2 | semidirect |
| 5. #20295280 | C2 | semidirect |
| 6. C4×D872 | C2 | semidirect |
| 7. #20295105 | C2 | semidirect |
| 8. #20295065 | C2 | semidirect |
| 9. #499×C109 | C2 | semidirect |
| 103. C109 | #3355 | semidirect |
| 105. #499 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295729 | 2 |
| #20295353 | 2 |
| #20295341 | 2 |
| #20295323 | 2 |
| #20295280 | 2 |
| C4×D872 | 2 |
| #20295105 | 2 |
| #20295065 | 2 |
| #499×C109 | 2 |
| #3355 | 109 |