Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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. #20293184 | C2 | semidirect |
| 3. #20292992 | C2 | semidirect |
| 4. #20292974 | C2 | semidirect |
| 5. #20292633 | C2 | semidirect |
| 6. C4×M16×C107 | C2 | semidirect |
| 9. #16812109 | C22 | semidirect |
| 13. #16812101 | C22 | semidirect |
| 17. #16812031 | C22 | semidirect |
| 20. #97×C107 | C22 | semidirect |
| 21. C4×C8×C107 | C22 | semidirect |
| 75. C107 | #3138 | semidirect |
| 81. C4×M16 | D107 | semidirect |
| 95. #97 | C2×D107 | semidirect |
| 96. C4×C8 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| C2×#16812106 | 2 |
| #20292992 | 2 |
| #20292974 | 2 |
| #20292633 | 2 |
| C4×M16×C107 | 2 |
| #3138 | 107 |