Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20292681 | C2 | semidirect |
| 3. #20292677 | C2 | semidirect |
| 4. #20292351 | C2 | semidirect |
| 5. #20292350 | C2 | semidirect |
| 6. #20292350 | C2 | semidirect |
| 7. #323×C107 | C2 | semidirect |
| 120. C107 | #1469 | semidirect |
| 127. #323 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812095 | 2 |
| #20292681 | 2 |
| #20292677 | 2 |
| #20292351 | 2 |
| #20292350 | 2 |
| #323×C107 | 2 |
| #1469 | 107 |