Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20295843 | C2 | semidirect |
| 2. #20295836 | C2 | semidirect |
| 3. #20295827 | C2 | semidirect |
| 4. #20295409 | C2 | semidirect |
| 5. #20295302 | C2 | semidirect |
| 6. #20295288 | C2 | semidirect |
| 7. #20295206 | C2 | semidirect |
| 8. #20295197 | C2 | semidirect |
| 9. #20295142 | C2 | semidirect |
| 10. #20295141 | C2 | semidirect |
| 11. #472×C109 | C2 | semidirect |
| 12. #16812746 | C22 | semidirect |
| 16. #16812732 | C22 | semidirect |
| 27. C2×Dic436 | C22 | semidirect |
| 28. C2×#13182017 | C22 | semidirect |
| 31. #16812707 | C22 | semidirect |
| 33. #16812686 | C22 | semidirect |
| 34. #16812634 | C22 | semidirect |
| 35. #16812626 | C22 | semidirect |
| 37. #16812625 | C22 | semidirect |
| 38. #16812617 | C22 | semidirect |
| 39. C8×Dic109 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C109 | C22 | semidirect |
| 42. #131×C109 | C22 | semidirect |
| 43. #108×C109 | C22 | semidirect |
| 44. #100×C109 | C22 | semidirect |
| 150. C109 | #3290 | semidirect |
| 156. #472 | D109 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D109 | semidirect |
| 185. #131 | C2×D109 | semidirect |
| 188. #108 | C2×D109 | semidirect |
| 193. #100 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295843 | 2 |
| #20295836 | 2 |
| #20295827 | 2 |
| #20295409 | 2 |
| #20295302 | 2 |
| #20295288 | 2 |
| #20295206 | 2 |
| #20295197 | 2 |
| #20295142 | 2 |
| #20295141 | 2 |
| #472×C109 | 2 |
| #3290 | 109 |