Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. #20294801 | C2 | semidirect |
| 5. C4×#13182004 | C2 | semidirect |
| 6. C16×Dic109 | C2 | semidirect |
| 7. #346×C109 | C2 | semidirect |
| 11. #16812638 | C4 | semidirect |
| 14. C16×D109 | C4 | semidirect |
| 61. C109 | #2108 | semidirect |
| 66. #346 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812638 | 2 |
| C2×C16×D109 | 2 |
| #20294980 | 2 |
| #20294801 | 2 |
| C4×#13182004 | 2 |
| C16×Dic109 | 2 |
| #346×C109 | 2 |
| #2108 | 109 |