Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20295576 | C2 | semidirect |
| 2. C4×#13182029 | C2 | semidirect |
| 3. #20295351 | C2 | semidirect |
| 4. #20295312 | C2 | semidirect |
| 5. #20295307 | C2 | semidirect |
| 6. #20295227 | C2 | semidirect |
| 7. #20295222 | C2 | semidirect |
| 8. #20295173 | C2 | semidirect |
| 9. #20295139 | C2 | semidirect |
| 10. #20295128 | C2 | semidirect |
| 11. #432×C109 | C2 | semidirect |
| 107. D436 | #41 | semidirect |
| 114. Dic218 | #41 | semidirect |
| 145. C109 | #3115 | semidirect |
| 156. #432 | D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295576 | 2 |
| C4×#13182029 | 2 |
| #20295351 | 2 |
| #20295312 | 2 |
| #20295307 | 2 |
| #20295227 | 2 |
| #20295222 | 2 |
| #20295173 | 2 |
| #20295139 | 2 |
| #20295128 | 2 |
| #432×C109 | 2 |
| #3115 | 109 |