Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20295429 | C2 | semidirect |
| 3. #20295364 | C2 | semidirect |
| 4. #20295339 | C2 | semidirect |
| 5. #20295321 | C2 | semidirect |
| 6. #20295313 | C2 | semidirect |
| 7. #20295274 | C2 | semidirect |
| 8. C4×#13182016 | C2 | semidirect |
| 9. #20295104 | C2 | semidirect |
| 10. #20295066 | C2 | semidirect |
| 11. #554×C109 | C2 | semidirect |
| 122. C109 | #3357 | semidirect |
| 124. #554 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295741 | 2 |
| #20295429 | 2 |
| #20295364 | 2 |
| #20295339 | 2 |
| #20295321 | 2 |
| #20295313 | 2 |
| #20295274 | 2 |
| C4×#13182016 | 2 |
| #20295104 | 2 |
| #20295066 | 2 |
| #554×C109 | 2 |
| #3357 | 109 |