Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. #20292733 | C2 | semidirect |
| 4. #20292442 | C2 | semidirect |
| 6. #20292404 | C2 | semidirect |
| 7. #365×C107 | C2 | semidirect |
| 12. Dic856 | C4 | semidirect |
| 13. #16812054 | C4 | semidirect |
| 65. C107 | #2180 | semidirect |
| 69. #365 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293070 | 2 |
| #20292748 | 2 |
| #20292733 | 2 |
| #20292442 | 2 |
| #20292436 | 2 |
| #20292404 | 2 |
| #365×C107 | 2 |
| #2180 | 107 |