Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. C2×#16812762 | C2 | semidirect |
| 4. #20295899 | C2 | semidirect |
| 16. #16812679 | C4 | semidirect |
| 17. #16812678 | C4 | semidirect |
| 20. #16812675 | C4 | semidirect |
| 24. C22⋊Q8×C109 | C4 | semidirect |
| 97. C22×C109 | #103 | semidirect |
| 103. C2×D109 | #103 | semidirect |
| 126. C109 | #1892 | semidirect |
| 143. C22⋊Q8 | #89137 | semidirect |
| 232. C22 | #16812762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D109⋊C8 | 2 |
| C2×#16812762 | 2 |
| #20295968 | 2 |
| #20295899 | 2 |
| C22⋊Q8×D109 | 2 |
| #1892 | 109 |