Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#16812725 | C2 | semidirect |
| 2. C22×#13182014 | C2 | semidirect |
| 3. #20295595 | C2 | semidirect |
| 4. #20295241 | C2 | semidirect |
| 5. #20295221 | C2 | semidirect |
| 6. #20295053 | C2 | semidirect |
| 7. #20295030 | C2 | semidirect |
| 8. #20295020 | C2 | semidirect |
| 9. #518×C109 | C2 | semidirect |
| 13. C2×#13182017 | C22 | semidirect |
| 16. C2×#13182014 | C22 | semidirect |
| 19. #16812696 | C22 | semidirect |
| 20. #16812687 | C22 | semidirect |
| 23. C4⋊#11724784 | C22 | semidirect |
| 24. #16812622 | C22 | semidirect |
| 25. #16812619 | C22 | semidirect |
| 26. #16812619 | C22 | semidirect |
| 29. C4×D4×C109 | C22 | semidirect |
| 56. C2×D4×C109 | D4 | semidirect |
| 122. C109 | #3041 | semidirect |
| 126. #518 | D109 | semidirect |
| 147. C4×D4 | C2×D109 | semidirect |
| 169. C2×D4 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812725 | 2 |
| C22×#13182014 | 2 |
| #20295595 | 2 |
| #20295241 | 2 |
| #20295221 | 2 |
| #20295053 | 2 |
| #20295030 | 2 |
| #20295020 | 2 |
| #518×C109 | 2 |
| #3041 | 109 |