Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 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. #20295432 | C2 | semidirect |
| 3. #20295418 | C2 | semidirect |
| 4. #20295394 | C2 | semidirect |
| 5. #20295388 | C2 | semidirect |
| 6. #20295282 | C2 | semidirect |
| 8. C4×#13182019 | C2 | semidirect |
| 9. C4×#13182016 | C2 | semidirect |
| 10. C4×#13182013 | C2 | semidirect |
| 11. #533×C109 | C2 | semidirect |
| 130. C109 | #3172 | semidirect |
| 131. #533 | 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 |
| #20295418 | 2 |
| #20295394 | 2 |
| #20295388 | 2 |
| #20295282 | 2 |
| #20295274 | 2 |
| C4×#13182019 | 2 |
| C4×#13182016 | 2 |
| C4×#13182013 | 2 |
| #533×C109 | 2 |
| #3172 | 109 |