Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #20293299 | C2 | semidirect |
| 2. #20292993 | C2 | semidirect |
| 3. #20292975 | C2 | semidirect |
| 4. #20292924 | C2 | semidirect |
| 5. #20292914 | C2 | semidirect |
| 6. #20292822 | C2 | semidirect |
| 7. #20292822 | C2 | semidirect |
| 8. #20292758 | C2 | semidirect |
| 9. #20292737 | C2 | semidirect |
| 10. C4×#13133803 | C2 | semidirect |
| 11. #554×C107 | C2 | semidirect |
| 80. D4×C107 | #41 | semidirect |
| 130. C107 | #3366 | semidirect |
| 131. #554 | D107 | semidirect |
| 218. D4 | #13133819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293299 | 2 |
| #20292993 | 2 |
| #20292975 | 2 |
| #20292924 | 2 |
| #20292914 | 2 |
| #20292822 | 2 |
| #20292758 | 2 |
| #20292737 | 2 |
| C4×#13133803 | 2 |
| #554×C107 | 2 |
| #3366 | 107 |