Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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. C22×C4×D109 | C4 | semidirect |
| 14. C2×C4⋊Dic109 | C4 | semidirect |
| 15. C2×#13182006 | C4 | semidirect |
| 17. C2×C42×C109 | C4 | semidirect |
| 51. C22×D109 | C4⋊C4 | semidirect |
| 66. C2×C4×C109 | C4⋊C4 | semidirect |
| 98. C4×C109 | #99 | semidirect |
| 110. C109 | #1799 | semidirect |
| 125. C2×C42 | #89137 | semidirect |
| 186. C2×C4 | C4⋊#89137 | semidirect |
| 210. C4 | #16812758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812758 | 2 |
| #20295968 | 2 |
| #20295904 | 2 |
| C2×C4×D436 | 2 |
| #1799 | 109 |