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 |
|---|---|---|
| 2. #20292993 | C2 | semidirect |
| 3. #20292975 | C2 | semidirect |
| 4. #20292631 | C2 | semidirect |
| 5. C4×#13133802 | C2 | semidirect |
| 6. #533×C107 | C2 | semidirect |
| 13. #16812029 | C22 | semidirect |
| 14. #16812020 | C22 | semidirect |
| 15. C4×C107⋊C8 | C22 | semidirect |
| 16. C4⋊Q8×C107 | C22 | semidirect |
| 17. #125×C107 | C22 | semidirect |
| 75. C107 | #3138 | semidirect |
| 76. #533 | D107 | semidirect |
| 85. C4⋊Q8 | C2×D107 | semidirect |
| 89. #125 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812106 | 2 |
| #20292993 | 2 |
| #20292975 | 2 |
| #20292631 | 2 |
| C4×#13133802 | 2 |
| #533×C107 | 2 |
| #3138 | 107 |