Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C2×#16812688 | C2 | semidirect |
| 3. #41×Dic109 | C2 | semidirect |
| 4. #20295250 | C2 | semidirect |
| 5. #20295243 | C2 | semidirect |
| 6. #20295049 | C2 | semidirect |
| 7. #20295035 | C2 | semidirect |
| 8. #20295032 | C2 | semidirect |
| 9. C2×#137×C109 | C2 | semidirect |
| 18. Q8×Dic109 | C22 | semidirect |
| 20. D4×Dic109 | C22 | semidirect |
| 26. #16812628 | C22 | semidirect |
| 27. #16812623 | C22 | semidirect |
| 32. C2×Q16×C109 | C22 | semidirect |
| 33. C2×SD16×C109 | C22 | semidirect |
| 126. C109 | #3040 | semidirect |
| 127. C2×#137 | D109 | semidirect |
| 141. C2×Q16 | C2×D109 | semidirect |
| 143. C2×SD16 | 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×#16812688 | 2 |
| #41×Dic109 | 2 |
| #20295250 | 2 |
| #20295243 | 2 |
| #20295049 | 2 |
| #20295035 | 2 |
| #20295032 | 2 |
| C2×#137×C109 | 2 |
| #3040 | 109 |