Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #20295364 | C2 | semidirect |
| 3. #20295318 | C2 | semidirect |
| 4. #20295313 | C2 | semidirect |
| 5. #20295233 | C2 | semidirect |
| 6. #20295228 | C2 | semidirect |
| 8. #20295131 | C2 | semidirect |
| 9. #20295124 | C2 | semidirect |
| 10. #20295083 | C2 | semidirect |
| 11. #533×C109 | C2 | semidirect |
| 137. C109 | #3116 | semidirect |
| 138. #533 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13182029 | 2 |
| #20295364 | 2 |
| #20295318 | 2 |
| #20295313 | 2 |
| #20295233 | 2 |
| #20295228 | 2 |
| #20295186 | 2 |
| #20295131 | 2 |
| #20295124 | 2 |
| #20295083 | 2 |
| #533×C109 | 2 |
| #3116 | 109 |