Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 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. #20296106 | C2 | semidirect |
| 2. #20296105 | C2 | semidirect |
| 3. C2×#16812787 | C2 | semidirect |
| 4. D109⋊#131 | C2 | semidirect |
| 6. #16812787 | C22 | semidirect |
| 7. #16812787 | C22 | semidirect |
| 8. #16812787 | C22 | semidirect |
| 9. #16812786 | C22 | semidirect |
| 10. #16812786 | C22 | semidirect |
| 11. C2×#13182039 | C22 | semidirect |
| 12. D109⋊M16 | C22 | semidirect |
| 13. C2×D109⋊C8 | C22 | semidirect |
| 59. C109 | #3573 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296106 | 2 |
| #20296105 | 2 |
| C2×#16812787 | 2 |
| D109⋊#131 | 2 |
| #20295863 | 2 |
| #3573 | 109 |