Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
260 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 64 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. D109⋊M32 | C2 | semidirect |
| 2. #20296036 | C2 | semidirect |
| 3. #20295938 | C2 | semidirect |
| 8. D109⋊C16 | C22 | semidirect |
| 9. #16812768 | C22 | semidirect |
| 12. C2×D872 | C4 | semidirect |
| 16. D8×D109 | C4 | semidirect |
| 19. C2×D8×C109 | C4 | semidirect |
| 90. C109 | #2140 | semidirect |
| 102. C2×D8 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D109⋊M32 | 2 |
| #20296036 | 2 |
| #20295938 | 2 |
| C2×D8×D109 | 2 |
| #2140 | 109 |