Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 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. #20295722 | C2 | semidirect |
| 2. #20295428 | C2 | semidirect |
| 3. #20295351 | C2 | semidirect |
| 4. #20295340 | C2 | semidirect |
| 5. #20295327 | C2 | semidirect |
| 6. #20295279 | C2 | semidirect |
| 7. C4×D872 | C2 | semidirect |
| 8. #20295068 | C2 | semidirect |
| 9. #436×C109 | C2 | semidirect |
| 103. C109 | #3355 | semidirect |
| 111. #436 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295722 | 2 |
| #20295428 | 2 |
| #20295351 | 2 |
| #20295340 | 2 |
| #20295327 | 2 |
| #20295279 | 2 |
| C4×D872 | 2 |
| #20295068 | 2 |
| #436×C109 | 2 |
| #3355 | 109 |