Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20295139 | C2 | semidirect |
| 3. #20294850 | C2 | semidirect |
| 4. #20294838 | C2 | semidirect |
| 5. #20294836 | C2 | semidirect |
| 6. #20294804 | C2 | semidirect |
| 7. #444×C109 | C2 | semidirect |
| 10. #16812642 | C4 | semidirect |
| 11. #16812640 | C4 | semidirect |
| 28. #13182004 | C2×C4 | semidirect |
| 30. Q16×C109 | C2×C4 | semidirect |
| 32. D8×C109 | C2×C4 | semidirect |
| 69. C109 | AGL(1,ℤ/16) | semidirect |
| 71. #444 | D109 | semidirect |
| 93. Q16 | C4×D109 | semidirect |
| 97. D8 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295461 | 2 |
| #20295139 | 2 |
| #20294850 | 2 |
| #20294838 | 2 |
| #20294836 | 2 |
| #20294804 | 2 |
| #444×C109 | 2 |
| AGL(1,ℤ/16) | 109 |