Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C4⋊Dic107 | C2 | semidirect |
| 2. #20292960 | C2 | semidirect |
| 3. #20292955 | C2 | semidirect |
| 4. #20292943 | C2 | semidirect |
| 5. #20292938 | C2 | semidirect |
| 6. #20292670 | C2 | semidirect |
| 7. #20292628 | C2 | semidirect |
| 8. #20292591 | C2 | semidirect |
| 18. #16812042 | C22 | semidirect |
| 19. #16812040 | C22 | semidirect |
| 20. #16812033 | C22 | semidirect |
| 21. #16812030 | C22 | semidirect |
| 131. C107 | #3092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic107 | 2 |
| #20292960 | 2 |
| #20292955 | 2 |
| #20292943 | 2 |
| #20292938 | 2 |
| #20292670 | 2 |
| #20292628 | 2 |
| #20292591 | 2 |
| #525×C107 | 2 |
| #3092 | 107 |