Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20293177 | C2 | semidirect |
| 2. #20292940 | C2 | semidirect |
| 3. #20292907 | C2 | semidirect |
| 4. #20292822 | C2 | semidirect |
| 5. #20292761 | C2 | semidirect |
| 6. C4×#13133803 | C2 | semidirect |
| 7. #20292680 | C2 | semidirect |
| 8. C2×C4×D4×C107 | C2 | semidirect |
| 11. #16812109 | C22 | semidirect |
| 12. #16812106 | C22 | semidirect |
| 17. C4×D428 | C22 | semidirect |
| 18. #16812042 | C22 | semidirect |
| 19. C4⋊(C107⋊C8) | C22 | semidirect |
| 21. #16812029 | C22 | semidirect |
| 23. C4×C107⋊C8 | C22 | semidirect |
| 73. D4×C107 | #41 | semidirect |
| 80. C2×C4×C107 | D8 | semidirect |
| 121. C107 | #3100 | semidirect |
| 123. C2×C4×D4 | D107 | semidirect |
| 199. D4 | #13133818 | semidirect |
| 208. C2×C4 | #13133803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293177 | 2 |
| #20292940 | 2 |
| #20292907 | 2 |
| #20292822 | 2 |
| #20292761 | 2 |
| C4×#13133803 | 2 |
| #20292680 | 2 |
| C2×C4×D4×C107 | 2 |
| #3100 | 107 |