Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20295053 | C2 | semidirect |
| 5. C2×#16812610 | C2 | semidirect |
| 6. #20294790 | C2 | semidirect |
| 7. #339×C109 | C2 | semidirect |
| 14. #16812622 | C4 | semidirect |
| 15. #16812619 | C4 | semidirect |
| 91. C109 | #1938 | semidirect |
| 98. #339 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295053 | 2 |
| C2×#16812627 | 2 |
| #20295020 | 2 |
| #20294994 | 2 |
| C2×#16812610 | 2 |
| #20294790 | 2 |
| #339×C109 | 2 |
| #1938 | 109 |