Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
326 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #20294990 | C2 | semidirect |
| 2. #20294889 | C2 | semidirect |
| 3. #20294760 | C2 | semidirect |
| 8. C22⋊#11724784 | C22 | semidirect |
| 10. #16812606 | C22 | semidirect |
| 12. C22×D4×C109 | C4 | semidirect |
| 16. #121×C109 | C4 | semidirect |
| 18. C2×C4⋊C4×C109 | C4 | semidirect |
| 103. C109 | #1510 | semidirect |
| 109. C22×D4 | Dic109 | semidirect |
| 114. #121 | Dic109 | semidirect |
| 116. C2×C4⋊C4 | Dic109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20294990 | 2 |
| #20294889 | 2 |
| #20294760 | 2 |
| C2×#121×C109 | 2 |
| #1510 | 109 |