Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812746 | C2 | semidirect |
| 2. C22×#13182017 | C2 | semidirect |
| 3. #20295593 | C2 | semidirect |
| 4. #20295168 | C2 | semidirect |
| 5. #20295163 | C2 | semidirect |
| 6. #20295036 | C2 | semidirect |
| 7. #20295022 | C2 | semidirect |
| 8. #20294994 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C109 | C2 | semidirect |
| 15. C2×#13182028 | C22 | semidirect |
| 18. C2×Q8×D109 | C22 | semidirect |
| 27. #16812624 | C22 | semidirect |
| 28. #16812623 | C22 | semidirect |
| 29. #16812620 | C22 | semidirect |
| 30. #16812611 | C22 | semidirect |
| 48. C2×Dic218 | D4 | semidirect |
| 69. #41×C109 | D4 | semidirect |
| 146. C109 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D109 | semidirect |
| 191. #41 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812746 | 2 |
| C22×#13182017 | 2 |
| #20295593 | 2 |
| #20295168 | 2 |
| #20295163 | 2 |
| #20295036 | 2 |
| #20295022 | 2 |
| #20294994 | 2 |
| C2×AGL(1,ℤ/8)×C109 | 2 |
| #3010 | 109 |