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×#16812724 | C2 | semidirect |
| 2. C2×#16812705 | C2 | semidirect |
| 3. #20295604 | C2 | semidirect |
| 4. #20295595 | C2 | semidirect |
| 5. #20295278 | C2 | semidirect |
| 6. #20295275 | C2 | semidirect |
| 7. #20295261 | C2 | semidirect |
| 8. #20295258 | C2 | semidirect |
| 9. #20295069 | C2 | semidirect |
| 10. C2×#16812621 | C2 | semidirect |
| 11. #416×C109 | C2 | semidirect |
| 19. C2×#13182012 | C22 | semidirect |
| 20. C2×C8×D109 | C22 | semidirect |
| 24. #16812675 | C22 | semidirect |
| 29. #16812670 | C22 | semidirect |
| 32. #16812632 | C22 | semidirect |
| 33. #16812630 | C22 | semidirect |
| 39. #103×C109 | C22 | semidirect |
| 40. #103×C109 | C22 | semidirect |
| 41. #102×C109 | C22 | semidirect |
| 42. #102×C109 | C22 | semidirect |
| 60. #13182013 | D4 | semidirect |
| 152. C109 | #3062 | semidirect |
| 162. #416 | D109 | semidirect |
| 189. #103 | C2×D109 | semidirect |
| 190. #103 | C2×D109 | semidirect |
| 193. #102 | C2×D109 | semidirect |
| 194. #102 | C2×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812724 | 2 |
| C2×#16812705 | 2 |
| #20295604 | 2 |
| #20295595 | 2 |
| #20295278 | 2 |
| #20295275 | 2 |
| #20295261 | 2 |
| #20295258 | 2 |
| #20295069 | 2 |
| C2×#16812621 | 2 |
| #416×C109 | 2 |
| #3062 | 109 |