Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#16812718 | C2 | semidirect |
| 2. C2×D8×D109 | C2 | semidirect |
| 3. #20295460 | C2 | direct (N × H) |
| 4. C2×#16812644 | C2 | semidirect |
| 5. C2×#16812643 | C2 | semidirect |
| 6. C2×#16812640 | C2 | semidirect |
| 7. C2×#16812638 | C2 | semidirect |
| 8. C2×D16×C109 | C2 | semidirect |
| 12. #16812718 | C22 | semidirect |
| 13. C2×Dic436 | C22 | semidirect |
| 18. D8×D109 | C22 | semidirect |
| 20. #16812644 | C22 | semidirect |
| 21. #16812643 | C22 | semidirect |
| 22. #16812640 | C22 | semidirect |
| 23. #16812638 | C22 | semidirect |
| 24. C2×#13182004 | C22 | semidirect |
| 26. C2×D8×C109 | C22 | semidirect |
| 27. D16×C109 | C22 | semidirect |
| 28. C2×C16×C109 | C22 | semidirect |
| 41. Dic436 | C23 | semidirect |
| 49. #13182004 | C23 | semidirect |
| 55. D8×C109 | C23 | semidirect |
| 57. C16×C109 | C23 | semidirect |
| 99. C2×C109 | #509 | semidirect |
| 104. C109 | C2×#509 | semidirect |
| 111. C2×D16 | D109 | semidirect |
| 124. C2×D8 | C2×D109 | semidirect |
| 129. D16 | C2×D109 | semidirect |
| 132. C2×C16 | C2×D109 | semidirect |
| 155. D8 | C22×D109 | semidirect |
| 161. C16 | C22×D109 | semidirect |
| 205. C2 | #20295460 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812718 | 2 |
| C2×D8×D109 | 2 |
| #20295460 | 2 |
| C2×#16812644 | 2 |
| C2×#16812643 | 2 |
| C2×#16812640 | 2 |
| C2×#16812638 | 2 |
| C2×D16×C109 | 2 |
| C2×#509 | 109 |