Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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. #20295968 | C2 | semidirect |
| 3. #20295904 | C2 | semidirect |
| 10. C23×Dic109 | C4 | semidirect |
| 14. C2×#13182008 | C4 | semidirect |
| 16. C2×C4×Dic109 | C4 | semidirect |
| 17. C2×C22⋊C4×C109 | C4 | semidirect |
| 48. C23×C109 | C4⋊C4 | semidirect |
| 74. C2×Dic109 | C4⋊C4 | semidirect |
| 100. Dic109 | #99 | semidirect |
| 110. C109 | #1799 | semidirect |
| 124. C2×C22⋊C4 | #89137 | semidirect |
| 164. C23 | C4⋊#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812757 | 2 |
| #20295968 | 2 |
| #20295904 | 2 |
| C2×#16812659 | 2 |
| #1799 | 109 |