Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #20295374 | C2 | semidirect |
| 3. #20295344 | C2 | semidirect |
| 4. #20295313 | C2 | semidirect |
| 5. #20295257 | C2 | semidirect |
| 6. #20295226 | C2 | semidirect |
| 7. #20295176 | C2 | semidirect |
| 8. C4×#13182016 | C2 | semidirect |
| 9. D4×#11724784 | C2 | semidirect |
| 10. C2×#16812619 | C2 | semidirect |
| 11. #554×C109 | C2 | semidirect |
| 15. C2×#13182016 | C22 | semidirect |
| 16. C22×#11724784 | C22 | semidirect |
| 22. #16812630 | C22 | semidirect |
| 23. #16812630 | C22 | semidirect |
| 24. C4⋊#11724784 | C22 | semidirect |
| 25. #16812623 | C22 | semidirect |
| 28. #16812619 | C22 | semidirect |
| 29. #16812619 | C22 | semidirect |
| 30. #16812619 | C22 | semidirect |
| 31. C22⋊#11724784 | C22 | semidirect |
| 32. C4×#11724784 | C22 | semidirect |
| 33. C4⋊Q8×C109 | C22 | semidirect |
| 36. C22⋊Q8×C109 | C22 | semidirect |
| 37. C4×Q8×C109 | C22 | semidirect |
| 40. C2×C4⋊C4×C109 | C22 | semidirect |
| 86. D4×C109 | SD16 | semidirect |
| 137. C109 | #3295 | semidirect |
| 138. #554 | D109 | semidirect |
| 154. C4⋊Q8 | C2×D109 | semidirect |
| 158. C22⋊Q8 | C2×D109 | semidirect |
| 162. C4×Q8 | C2×D109 | semidirect |
| 166. C2×C4⋊C4 | C2×D109 | semidirect |
| 231. D4 | #13182016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D436 | 2 |
| #20295374 | 2 |
| #20295344 | 2 |
| #20295313 | 2 |
| #20295257 | 2 |
| #20295226 | 2 |
| #20295176 | 2 |
| C4×#13182016 | 2 |
| D4×#11724784 | 2 |
| C2×#16812619 | 2 |
| #554×C109 | 2 |
| #3295 | 109 |