Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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. #20292494 | C2 | semidirect |
| 3. #20292491 | C2 | semidirect |
| 6. C4×Dic107⋊C4 | C2 | semidirect |
| 8. #20292473 | C2 | semidirect |
| 9. #376×C107 | C2 | semidirect |
| 19. C42×D107 | C4 | semidirect |
| 99. C107 | #2283 | semidirect |
| 108. #376 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D107 | 2 |
| #20292494 | 2 |
| #20292491 | 2 |
| #20292489 | 2 |
| #20292486 | 2 |
| C4×Dic107⋊C4 | 2 |
| C4×(C2×D107)⋊C4 | 2 |
| #20292473 | 2 |
| #376×C107 | 2 |
| #2283 | 107 |