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. C22×#13182014 | C2 | semidirect |
| 3. #20295593 | C2 | semidirect |
| 4. #20295170 | C2 | semidirect |
| 5. #20295158 | C2 | semidirect |
| 6. #20295032 | C2 | semidirect |
| 7. #20295022 | C2 | semidirect |
| 8. #20294994 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C109 | C2 | semidirect |
| 12. C2×#13182030 | C22 | semidirect |
| 18. C2×D4×D109 | C22 | semidirect |
| 20. C2×#13182014 | C22 | semidirect |
| 21. C22×#11724784 | C22 | semidirect |
| 24. #16812670 | C22 | semidirect |
| 26. #16812658 | C22 | semidirect |
| 27. #16812623 | C22 | semidirect |
| 28. #16812621 | C22 | semidirect |
| 29. #16812620 | C22 | semidirect |
| 30. #16812611 | C22 | semidirect |
| 32. C22×D4×C109 | C22 | semidirect |
| 34. C2×SD16×C109 | C22 | semidirect |
| 35. C2×D8×C109 | C22 | semidirect |
| 36. C2×M16×C109 | C22 | semidirect |
| 50. C2×D436 | D4 | semidirect |
| 69. #41×C109 | D4 | semidirect |
| 152. C109 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D109 | semidirect |
| 172. C22×D4 | C2×D109 | semidirect |
| 174. C2×SD16 | C2×D109 | semidirect |
| 177. C2×D8 | C2×D109 | semidirect |
| 178. C2×M16 | C2×D109 | semidirect |
| 198. #41 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812745 | 2 |
| C22×#13182014 | 2 |
| #20295593 | 2 |
| #20295170 | 2 |
| #20295158 | 2 |
| #20295032 | 2 |
| #20295022 | 2 |
| #20294994 | 2 |
| C2×AGL(1,ℤ/8)×C109 | 2 |
| #3008 | 109 |