Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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×#13182018 | C2 | semidirect |
| 2. C2×#16812705 | C2 | semidirect |
| 3. #20295602 | C2 | semidirect |
| 5. #20295273 | C2 | semidirect |
| 6. #20295256 | C2 | semidirect |
| 7. #20295034 | C2 | semidirect |
| 8. #20295030 | C2 | semidirect |
| 9. #427×C109 | C2 | semidirect |
| 18. C2×#13182012 | C22 | semidirect |
| 19. C2×C8×D109 | C22 | semidirect |
| 25. #16812679 | C22 | semidirect |
| 28. #16812622 | C22 | semidirect |
| 33. #107×C109 | C22 | semidirect |
| 34. #106×C109 | C22 | semidirect |
| 62. C2×C8×C109 | D4 | semidirect |
| 121. C109 | #3057 | semidirect |
| 128. #427 | D109 | semidirect |
| 152. #107 | C2×D109 | semidirect |
| 153. #106 | C2×D109 | semidirect |
| 180. C2×C8 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182018 | 2 |
| C2×#16812705 | 2 |
| #20295602 | 2 |
| #20295595 | 2 |
| #20295273 | 2 |
| #20295256 | 2 |
| #20295034 | 2 |
| #20295030 | 2 |
| #427×C109 | 2 |
| #3057 | 109 |