Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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×#16812787 | C2 | semidirect |
| 2. C2×#16812786 | C2 | semidirect |
| 3. #20296069 | C2 | direct (N × H) |
| 4. C2×#16812769 | C2 | semidirect |
| 5. C2×#16812764 | C2 | semidirect |
| 6. C2×#16812763 | C2 | semidirect |
| 7. C2×C8×#89137 | C2 | semidirect |
| 10. #16812787 | C22 | semidirect |
| 12. #16812786 | C22 | semidirect |
| 21. #16812769 | C22 | semidirect |
| 22. #16812764 | C22 | semidirect |
| 23. #16812763 | C22 | semidirect |
| 24. C8×#89137 | C22 | semidirect |
| 27. #16812720 | C4 | semidirect |
| 29. C2×#13182019 | C4 | semidirect |
| 30. C2×#13182018 | C4 | semidirect |
| 31. C2×#13182014 | C4 | semidirect |
| 33. C2×SD16×C109 | C4 | semidirect |
| 66. #13182019 | C2×C4 | semidirect |
| 67. #13182018 | C2×C4 | semidirect |
| 68. #13182014 | C2×C4 | semidirect |
| 74. SD16×C109 | C2×C4 | semidirect |
| 127. C2×C109 | #443 | semidirect |
| 133. C109 | C2×#443 | semidirect |
| 148. C2×SD16 | #89137 | semidirect |
| 187. SD16 | C2×#89137 | semidirect |
| 263. C2 | #20296069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812787 | 2 |
| C2×#16812786 | 2 |
| #20296069 | 2 |
| C2×#16812769 | 2 |
| C2×#16812764 | 2 |
| C2×#16812763 | 2 |
| C2×C8×#89137 | 2 |
| C2×#16812720 | 2 |
| C2×#443 | 109 |