Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#16812770 | C2 | semidirect |
| 2. #20296036 | C2 | semidirect |
| 4. #20295909 | C2 | semidirect |
| 16. #16812707 | C4 | semidirect |
| 17. #16812706 | C4 | semidirect |
| 19. #16812705 | C4 | semidirect |
| 24. #131×C109 | C4 | semidirect |
| 112. C109 | #1814 | semidirect |
| 124. #131 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812770 | 2 |
| #20296036 | 2 |
| #20296023 | 2 |
| #20295909 | 2 |
| #131×D109 | 2 |
| #1814 | 109 |