Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#13182014 | C2 | semidirect |
| 2. #20295590 | C2 | semidirect |
| 3. #20295501 | C2 | semidirect |
| 4. #20295243 | C2 | semidirect |
| 5. #20295219 | C2 | semidirect |
| 6. #20295054 | C2 | semidirect |
| 7. #20295032 | C2 | semidirect |
| 8. #20295022 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C109 | C2 | semidirect |
| 14. #16812695 | C22 | semidirect |
| 15. #16812688 | C22 | semidirect |
| 19. D4×Dic109 | C22 | semidirect |
| 23. #16812628 | C22 | semidirect |
| 24. #16812623 | C22 | semidirect |
| 25. #16812621 | C22 | semidirect |
| 26. #16812620 | C22 | semidirect |
| 30. C2×SD16×C109 | C22 | semidirect |
| 31. C2×D8×C109 | C22 | semidirect |
| 58. C2×D4×C109 | D4 | semidirect |
| 122. C109 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D109 | semidirect |
| 136. C2×SD16 | C2×D109 | semidirect |
| 139. C2×D8 | C2×D109 | semidirect |
| 168. C2×D4 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182014 | 2 |
| #20295590 | 2 |
| #20295501 | 2 |
| #20295243 | 2 |
| #20295219 | 2 |
| #20295054 | 2 |
| #20295032 | 2 |
| #20295022 | 2 |
| C2×AGL(1,ℤ/8)×C109 | 2 |
| #3041 | 109 |