Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#16812705 | C2 | semidirect |
| 3. #20295607 | C2 | semidirect |
| 4. #20295593 | C2 | semidirect |
| 5. #20295278 | C2 | semidirect |
| 6. #20295271 | C2 | semidirect |
| 7. #20295261 | C2 | semidirect |
| 8. #20295254 | C2 | semidirect |
| 9. #20295066 | C2 | semidirect |
| 10. #20295023 | C2 | semidirect |
| 11. C2×#102×C109 | C2 | semidirect |
| 19. C2×#13182012 | C22 | semidirect |
| 20. C2×C8×D109 | C22 | semidirect |
| 24. #16812679 | C22 | semidirect |
| 26. #16812674 | C22 | semidirect |
| 32. #16812632 | C22 | semidirect |
| 33. #16812630 | C22 | semidirect |
| 34. #16812624 | C22 | semidirect |
| 35. #16812624 | C22 | semidirect |
| 36. #16812621 | C22 | semidirect |
| 37. #16812621 | C22 | semidirect |
| 60. #13182013 | D4 | semidirect |
| 152. C109 | #3062 | semidirect |
| 163. C2×#102 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812725 | 2 |
| C2×#16812705 | 2 |
| #20295607 | 2 |
| #20295593 | 2 |
| #20295278 | 2 |
| #20295271 | 2 |
| #20295261 | 2 |
| #20295254 | 2 |
| #20295066 | 2 |
| #20295023 | 2 |
| C2×#102×C109 | 2 |
| #3062 | 109 |