Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#16812732 | C2 | semidirect |
| 3. #20295597 | C2 | semidirect |
| 4. #20295211 | C2 | semidirect |
| 5. #20295206 | C2 | semidirect |
| 6. #20295042 | C2 | semidirect |
| 7. #413×C109 | C2 | semidirect |
| 16. C22×Dic218 | C22 | semidirect |
| 18. #16812732 | C22 | semidirect |
| 21. #16812697 | C22 | semidirect |
| 22. #16812686 | C22 | semidirect |
| 25. #16812658 | C22 | semidirect |
| 26. #16812625 | C22 | semidirect |
| 28. C2×M16×C109 | C22 | semidirect |
| 29. #101×C109 | C22 | semidirect |
| 30. #100×C109 | C22 | semidirect |
| 130. C109 | #3022 | semidirect |
| 137. #413 | D109 | semidirect |
| 152. C2×M16 | C2×D109 | semidirect |
| 159. #101 | C2×D109 | semidirect |
| 160. #100 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295862 | 2 |
| C2×#16812732 | 2 |
| #20295597 | 2 |
| #20295211 | 2 |
| #20295206 | 2 |
| #20295042 | 2 |
| #413×C109 | 2 |
| #3022 | 109 |