Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D109 | C2 | semidirect |
| 3. C2×#16812675 | C2 | semidirect |
| 4. #20295281 | C2 | semidirect |
| 5. #20295269 | C2 | semidirect |
| 6. #20295264 | C2 | semidirect |
| 7. #20295252 | C2 | semidirect |
| 8. #20295068 | C2 | semidirect |
| 9. #20295035 | C2 | semidirect |
| 10. #20295027 | C2 | semidirect |
| 11. C2×#137×C109 | C2 | semidirect |
| 33. #16812633 | C22 | semidirect |
| 34. #16812631 | C22 | semidirect |
| 35. #16812623 | C22 | semidirect |
| 36. #16812623 | C22 | semidirect |
| 37. #16812623 | C22 | semidirect |
| 38. #16812620 | C22 | semidirect |
| 42. C2×Q16×C109 | C22 | semidirect |
| 43. C2×SD16×C109 | C22 | semidirect |
| 90. M16×C109 | D4 | semidirect |
| 145. C2×D109 | #137 | semidirect |
| 164. C109 | #3056 | semidirect |
| 165. C2×#137 | D109 | semidirect |
| 180. C2×Q16 | C2×D109 | semidirect |
| 181. C2×SD16 | C2×D109 | semidirect |
| 236. M16 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D109 | 2 |
| #20295533 | 2 |
| C2×#16812675 | 2 |
| #20295281 | 2 |
| #20295269 | 2 |
| #20295264 | 2 |
| #20295252 | 2 |
| #20295068 | 2 |
| #20295035 | 2 |
| #20295027 | 2 |
| C2×#137×C109 | 2 |
| #3056 | 109 |