Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20294923 | C2 | semidirect |
| 4. #20294920 | C2 | semidirect |
| 5. #20294914 | C2 | semidirect |
| 6. #20294908 | C2 | semidirect |
| 7. #20294899 | C2 | semidirect |
| 8. #20294884 | C2 | semidirect |
| 11. #16812680 | C4 | semidirect |
| 34. C22×Dic109 | C2×C4 | semidirect |
| 43. #13182008 | C2×C4 | semidirect |
| 47. C22⋊Dic109 | C2×C4 | semidirect |
| 127. C109 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812680 | 2 |
| #20294929 | 2 |
| #20294923 | 2 |
| #20294920 | 2 |
| #20294914 | 2 |
| #20294908 | 2 |
| #20294899 | 2 |
| #20294884 | 2 |
| #386×C109 | 2 |
| #2376 | 109 |