Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#16812727 | C2 | semidirect |
| 2. #20295604 | C2 | semidirect |
| 3. #20295590 | C2 | semidirect |
| 4. #20295279 | C2 | semidirect |
| 5. #20295272 | C2 | semidirect |
| 6. #20295262 | C2 | semidirect |
| 7. #20295255 | C2 | semidirect |
| 8. #20295068 | C2 | semidirect |
| 9. #20295023 | C2 | semidirect |
| 10. C2×#16812621 | C2 | semidirect |
| 11. C2×#131×C109 | C2 | semidirect |
| 19. #16812678 | C22 | semidirect |
| 23. #16812673 | C22 | semidirect |
| 29. #16812633 | C22 | semidirect |
| 30. #16812631 | C22 | semidirect |
| 31. #16812624 | C22 | semidirect |
| 32. #16812624 | C22 | semidirect |
| 35. #16812621 | C22 | semidirect |
| 36. #16812621 | C22 | semidirect |
| 40. C2×M16×C109 | C22 | semidirect |
| 42. C22×C8×C109 | C22 | semidirect |
| 79. M16×C109 | D4 | semidirect |
| 152. C109 | #3062 | semidirect |
| 154. C2×#131 | D109 | semidirect |
| 172. C2×M16 | C2×D109 | semidirect |
| 174. C22×C8 | C2×D109 | semidirect |
| 220. M16 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812727 | 2 |
| #20295604 | 2 |
| #20295590 | 2 |
| #20295279 | 2 |
| #20295272 | 2 |
| #20295262 | 2 |
| #20295255 | 2 |
| #20295068 | 2 |
| #20295023 | 2 |
| C2×#16812621 | 2 |
| C2×#131×C109 | 2 |
| #3062 | 109 |