Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20293101 | C2 | semidirect |
| 3. #20292644 | C2 | semidirect |
| 4. #20292631 | C2 | semidirect |
| 5. #20292397 | C2 | semidirect |
| 6. #20292383 | C2 | semidirect |
| 7. #410×C107 | C2 | semidirect |
| 11. C2×#13133805 | C4 | semidirect |
| 12. C2×#13133803 | C4 | semidirect |
| 40. C2×C107⋊C8 | C2×C4 | semidirect |
| 49. C2×Q8×C107 | C2×C4 | semidirect |
| 51. C2×D4×C107 | C2×C4 | semidirect |
| 116. C107 | #1904 | semidirect |
| 121. #410 | D107 | semidirect |
| 146. C2×Q8 | C4×D107 | semidirect |
| 154. C2×D4 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812134 | 2 |
| #20293101 | 2 |
| #20292644 | 2 |
| #20292631 | 2 |
| #20292397 | 2 |
| #20292383 | 2 |
| #410×C107 | 2 |
| #1904 | 107 |