Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #20296072 | C2 | semidirect |
| 2. #20296067 | C2 | semidirect |
| 3. #20295951 | C2 | semidirect |
| 4. #20295944 | C2 | semidirect |
| 5. #20295943 | C2 | semidirect |
| 6. #20295916 | C2 | semidirect |
| 18. #16812642 | C4 | semidirect |
| 19. D1744 | C4 | semidirect |
| 20. #16812640 | C4 | semidirect |
| 22. SD32×C109 | C4 | semidirect |
| 36. D872 | C2×C4 | semidirect |
| 39. #13182004 | C2×C4 | semidirect |
| 40. Q16×C109 | C2×C4 | semidirect |
| 42. C16×C109 | C2×C4 | semidirect |
| 76. C109 | AGL(1,ℤ/16) | semidirect |
| 89. SD32 | #89137 | semidirect |
| 102. Q16 | C2×#89137 | semidirect |
| 118. C16 | C2×#89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296072 | 2 |
| #20296067 | 2 |
| #20295951 | 2 |
| #20295944 | 2 |
| #20295943 | 2 |
| #20295916 | 2 |
| #20295463 | 2 |
| AGL(1,ℤ/16) | 109 |