Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
540 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20294930 | C2 | semidirect |
| 3. #20294917 | C2 | semidirect |
| 4. #20294916 | C2 | semidirect |
| 6. #20294897 | C2 | semidirect |
| 7. #20294894 | C2 | semidirect |
| 8. C4×#13182006 | C2 | semidirect |
| 9. C4×C4⋊C4×C109 | C2 | semidirect |
| 13. #16812687 | C4 | semidirect |
| 34. C2×Dic218 | C2×C4 | semidirect |
| 47. #13182006 | C2×C4 | semidirect |
| 48. #13182006 | C2×C4 | semidirect |
| 58. C42×C109 | C2×C4 | semidirect |
| 119. C109 | #2337 | semidirect |
| 127. C4×C4⋊C4 | D109 | semidirect |
| 177. C42 | C4×D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812687 | 2 |
| #20294930 | 2 |
| #20294917 | 2 |
| #20294916 | 2 |
| #20294904 | 2 |
| #20294897 | 2 |
| #20294894 | 2 |
| C4×#13182006 | 2 |
| C4×C4⋊C4×C109 | 2 |
| #2337 | 109 |