Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #20295654 | C2 | semidirect |
| 3. #20295393 | C2 | semidirect |
| 4. #20295387 | C2 | semidirect |
| 5. #20295382 | C2 | semidirect |
| 6. #20295375 | C2 | semidirect |
| 9. C2×#16812623 | C2 | semidirect |
| 10. #20294984 | C2 | semidirect |
| 11. #419×C109 | C2 | semidirect |
| 128. C109 | #3137 | semidirect |
| 135. #419 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295654 | 2 |
| #20295600 | 2 |
| #20295393 | 2 |
| #20295387 | 2 |
| #20295382 | 2 |
| #20295375 | 2 |
| #20295028 | 2 |
| #20295020 | 2 |
| C2×#16812623 | 2 |
| #20294984 | 2 |
| #419×C109 | 2 |
| #3137 | 109 |