Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295581 | C2 | semidirect |
| 3. #20295389 | C2 | semidirect |
| 4. #20295374 | C2 | semidirect |
| 5. #20295373 | C2 | semidirect |
| 6. #20295372 | C2 | semidirect |
| 7. #20295029 | C2 | semidirect |
| 8. C4×#13182012 | C2 | semidirect |
| 9. #486×C109 | C2 | semidirect |
| 14. #16812699 | C22 | semidirect |
| 19. #16812690 | C22 | semidirect |
| 26. #16812621 | C22 | semidirect |
| 27. #16812620 | C22 | semidirect |
| 28. #16812619 | C22 | semidirect |
| 29. #16812609 | C22 | semidirect |
| 30. C4×#11724784 | C22 | semidirect |
| 31. C4⋊Q8×C109 | C22 | semidirect |
| 33. #102×C109 | C22 | semidirect |
| 34. C4×C8×C109 | C22 | semidirect |
| 124. C109 | #3138 | semidirect |
| 131. #486 | D109 | semidirect |
| 139. C4⋊Q8 | C2×D109 | semidirect |
| 155. #102 | C2×D109 | semidirect |
| 158. C4×C8 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295581 | 2 |
| #127×D109 | 2 |
| #20295389 | 2 |
| #20295374 | 2 |
| #20295373 | 2 |
| #20295372 | 2 |
| #20295029 | 2 |
| C4×#13182012 | 2 |
| #486×C109 | 2 |
| #3138 | 109 |