Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20295503 | C2 | semidirect |
| 4. #20295128 | C2 | semidirect |
| 5. C4×#13182018 | C2 | semidirect |
| 6. #20295064 | C2 | semidirect |
| 7. #20295036 | C2 | semidirect |
| 9. #405×C109 | C2 | semidirect |
| 12. C2×#13182018 | C4 | semidirect |
| 15. C4×Dic218 | C22 | semidirect |
| 23. #16812633 | C22 | semidirect |
| 24. #16812631 | C22 | semidirect |
| 25. #16812624 | C22 | semidirect |
| 30. #97×C109 | C22 | semidirect |
| 31. C4×C8×C109 | C22 | semidirect |
| 35. C2×Dic218 | C2×C4 | semidirect |
| 43. #13182018 | C2×C4 | semidirect |
| 44. #13182018 | C2×C4 | semidirect |
| 56. C2×C8×C109 | C2×C4 | semidirect |
| 104. C109 | #2949 | semidirect |
| 113. #405 | D109 | semidirect |
| 134. #97 | C2×D109 | semidirect |
| 135. C4×C8 | C2×D109 | semidirect |
| 151. C2×C8 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182018 | 2 |
| #20295503 | 2 |
| #20295500 | 2 |
| #20295128 | 2 |
| C4×#13182018 | 2 |
| #20295064 | 2 |
| #20295036 | 2 |
| #20295032 | 2 |
| #405×C109 | 2 |
| #2949 | 109 |