Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #20292582 | C2 | semidirect |
| 5. #20292392 | C2 | semidirect |
| 6. #20292387 | C2 | semidirect |
| 7. C2×C4×C8×C107 | C2 | semidirect |
| 10. #16812115 | C4 | semidirect |
| 16. #16812037 | C4 | semidirect |
| 17. #16812034 | C4 | semidirect |
| 18. #16812031 | C4 | semidirect |
| 99. C107 | #1764 | semidirect |
| 104. C2×C4×C8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812115 | 2 |
| C2×#16812037 | 2 |
| #20292624 | 2 |
| #20292582 | 2 |
| #20292392 | 2 |
| #20292387 | 2 |
| C2×C4×C8×C107 | 2 |
| #1764 | 107 |