Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#16812745 | C2 | semidirect |
| 2. C2×#16812727 | C2 | semidirect |
| 3. C22×D872 | C2 | semidirect |
| 4. #20295590 | C2 | semidirect |
| 5. #20295173 | C2 | semidirect |
| 6. #20295162 | C2 | semidirect |
| 7. #20295032 | C2 | semidirect |
| 8. #20295023 | C2 | semidirect |
| 9. #408×C109 | C2 | semidirect |
| 14. C2×#13182029 | C22 | semidirect |
| 16. C22×D436 | C22 | semidirect |
| 17. C22×D436 | C22 | semidirect |
| 21. C2×#13182018 | C22 | semidirect |
| 23. C2×D872 | C22 | semidirect |
| 24. C2×D872 | C22 | semidirect |
| 27. #16812673 | C22 | semidirect |
| 29. #16812658 | C22 | semidirect |
| 30. #16812624 | C22 | semidirect |
| 31. #16812621 | C22 | semidirect |
| 32. #16812621 | C22 | semidirect |
| 34. C2×M16×C109 | C22 | semidirect |
| 35. C22×C8×C109 | C22 | semidirect |
| 36. C22⋊C8×C109 | C22 | semidirect |
| 44. #13182029 | D4 | semidirect |
| 54. C2×D436 | D4 | semidirect |
| 152. C109 | #3008 | semidirect |
| 161. #408 | D109 | semidirect |
| 178. C2×M16 | C2×D109 | semidirect |
| 179. C22×C8 | C2×D109 | semidirect |
| 188. C22⋊C8 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812745 | 2 |
| C2×#16812727 | 2 |
| C22×D872 | 2 |
| #20295590 | 2 |
| #20295173 | 2 |
| #20295162 | 2 |
| #20295032 | 2 |
| #20295023 | 2 |
| #408×C109 | 2 |
| #3008 | 109 |