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. C2×#16812724 | C2 | semidirect |
| 3. C22×#13182018 | C2 | semidirect |
| 4. #20295595 | C2 | semidirect |
| 5. #20295172 | C2 | semidirect |
| 6. #20295166 | C2 | semidirect |
| 7. #20295034 | C2 | semidirect |
| 8. #20294992 | C2 | semidirect |
| 9. #416×C109 | C2 | semidirect |
| 15. C2×#13182028 | C22 | semidirect |
| 18. C2×Q8×D109 | C22 | semidirect |
| 30. #16812622 | C22 | semidirect |
| 31. #16812611 | C22 | semidirect |
| 35. #103×C109 | C22 | semidirect |
| 36. #102×C109 | C22 | semidirect |
| 49. C2×Dic218 | D4 | semidirect |
| 72. #41×C109 | D4 | semidirect |
| 146. C109 | #3010 | semidirect |
| 154. #416 | D109 | semidirect |
| 180. #103 | C2×D109 | semidirect |
| 181. #102 | C2×D109 | semidirect |
| 191. #41 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812746 | 2 |
| C2×#16812724 | 2 |
| C22×#13182018 | 2 |
| #20295595 | 2 |
| #20295172 | 2 |
| #20295166 | 2 |
| #20295034 | 2 |
| #20294992 | 2 |
| #416×C109 | 2 |
| #3010 | 109 |