Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20295825 | C2 | semidirect |
| 2. C2×#16812722 | C2 | semidirect |
| 3. #131×D109 | C2 | semidirect |
| 4. #20295298 | C2 | semidirect |
| 5. #20295297 | C2 | semidirect |
| 6. #20295296 | C2 | semidirect |
| 7. #20295292 | C2 | semidirect |
| 8. #20295291 | C2 | semidirect |
| 9. #108×D109 | C2 | semidirect |
| 10. #20295009 | C2 | semidirect |
| 11. #473×C109 | C2 | semidirect |
| 25. C2×#13182016 | C22 | semidirect |
| 26. C2×D872 | C22 | semidirect |
| 37. #16812635 | C22 | semidirect |
| 38. #16812634 | C22 | semidirect |
| 39. #16812618 | C22 | semidirect |
| 40. #16812615 | C22 | semidirect |
| 41. #16812615 | C22 | semidirect |
| 43. C2×Q16×C109 | C22 | semidirect |
| 45. #108×C109 | C22 | semidirect |
| 46. #101×C109 | C22 | semidirect |
| 167. C109 | #3067 | semidirect |
| 172. #473 | D109 | semidirect |
| 193. C2×Q16 | C2×D109 | semidirect |
| 209. #108 | C2×D109 | semidirect |
| 211. #101 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295825 | 2 |
| C2×#16812722 | 2 |
| #131×D109 | 2 |
| #20295298 | 2 |
| #20295297 | 2 |
| #20295296 | 2 |
| #20295292 | 2 |
| #20295291 | 2 |
| #108×D109 | 2 |
| #20295009 | 2 |
| #473×C109 | 2 |
| #3067 | 109 |