Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
348 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 3. C2×C8×Dic109 | C2 | semidirect |
| 5. #20294781 | C2 | semidirect |
| 6. #20294780 | C2 | semidirect |
| 7. C2×#97×C109 | C2 | semidirect |
| 11. C2×#13182012 | C4 | semidirect |
| 16. #16812611 | C4 | semidirect |
| 72. C2×Dic109 | M16 | semidirect |
| 78. C8×C109 | C22⋊C4 | semidirect |
| 105. C109 | #1753 | semidirect |
| 108. C2×#97 | D109 | semidirect |
| 185. C8 | #13182006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182012 | 2 |
| C2×#16812611 | 2 |
| C2×C8×Dic109 | 2 |
| C4×#13182006 | 2 |
| #20294781 | 2 |
| #20294780 | 2 |
| C2×#97×C109 | 2 |
| #1753 | 109 |