Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20293174 | C2 | semidirect |
| 2. #20293031 | C2 | semidirect |
| 3. #20293002 | C2 | semidirect |
| 4. #20292972 | C2 | semidirect |
| 5. #20292864 | C2 | semidirect |
| 6. #20292862 | C2 | semidirect |
| 7. #20292860 | C2 | semidirect |
| 8. C4×D856 | C2 | semidirect |
| 9. C4×#13133803 | C2 | semidirect |
| 10. C4×C8×D107 | C2 | semidirect |
| 11. C4×D8×C107 | C2 | semidirect |
| 96. C4×D107 | D8 | semidirect |
| 99. C8×C107 | #41 | semidirect |
| 101. C107⋊C8 | #41 | semidirect |
| 128. C107 | #3169 | semidirect |
| 138. C4×D8 | D107 | semidirect |
| 229. C8 | #13133818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293174 | 2 |
| #20293031 | 2 |
| #20293002 | 2 |
| #20292972 | 2 |
| #20292864 | 2 |
| #20292862 | 2 |
| #20292860 | 2 |
| C4×D856 | 2 |
| C4×#13133803 | 2 |
| C4×C8×D107 | 2 |
| C4×D8×C107 | 2 |
| #3169 | 107 |