Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#16812730 | C2 | semidirect |
| 2. C2×#16812724 | C2 | semidirect |
| 3. C2×#16812719 | C2 | semidirect |
| 4. C22×#13182016 | C2 | semidirect |
| 5. #20295595 | C2 | semidirect |
| 6. #20295418 | C2 | semidirect |
| 7. #20295416 | C2 | semidirect |
| 8. #20295408 | C2 | semidirect |
| 9. #20295400 | C2 | semidirect |
| 10. #20294982 | C2 | semidirect |
| 11. #536×C109 | C2 | semidirect |
| 17. C2×#13182019 | C22 | semidirect |
| 18. C2×#13182019 | C22 | semidirect |
| 19. C2×#13182017 | C22 | semidirect |
| 24. C2×#13182016 | C22 | semidirect |
| 25. C2×#13182016 | C22 | semidirect |
| 27. C2×#13182014 | C22 | semidirect |
| 34. #16812610 | C22 | semidirect |
| 35. C4×#11724784 | C22 | semidirect |
| 38. C4⋊Q8×C109 | C22 | semidirect |
| 39. #124×C109 | C22 | semidirect |
| 65. #13182013 | D4 | semidirect |
| 66. C2×#11724784 | D4 | semidirect |
| 149. C109 | #3154 | semidirect |
| 154. #536 | D109 | semidirect |
| 181. C4⋊Q8 | C2×D109 | semidirect |
| 184. #124 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812730 | 2 |
| C2×#16812724 | 2 |
| C2×#16812719 | 2 |
| C22×#13182016 | 2 |
| #20295595 | 2 |
| #20295418 | 2 |
| #20295416 | 2 |
| #20295408 | 2 |
| #20295400 | 2 |
| #20294982 | 2 |
| #536×C109 | 2 |
| #3154 | 109 |