Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 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. #20295500 | C2 | semidirect |
| 3. #20295139 | C2 | semidirect |
| 4. C4×D872 | C2 | semidirect |
| 5. #20295064 | C2 | semidirect |
| 6. #20295032 | C2 | semidirect |
| 7. #405×C109 | C2 | semidirect |
| 9. C2×D872 | C4 | semidirect |
| 12. C4×D436 | C22 | semidirect |
| 16. #16812633 | C22 | semidirect |
| 17. #16812631 | C22 | semidirect |
| 18. #16812621 | C22 | semidirect |
| 22. #97×C109 | C22 | semidirect |
| 23. C4×C8×C109 | C22 | semidirect |
| 27. C2×D436 | C2×C4 | semidirect |
| 30. D872 | C2×C4 | semidirect |
| 31. D872 | C2×C4 | semidirect |
| 38. C2×C8×C109 | C2×C4 | semidirect |
| 78. C109 | #2948 | semidirect |
| 85. #405 | D109 | semidirect |
| 100. #97 | C2×D109 | semidirect |
| 101. C4×C8 | C2×D109 | semidirect |
| 112. 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×D872 | 2 |
| #20295500 | 2 |
| #20295139 | 2 |
| C4×D872 | 2 |
| #20295064 | 2 |
| #20295032 | 2 |
| #405×C109 | 2 |
| #2948 | 109 |