Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 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. #20292663 | C2 | semidirect |
| 3. #20292643 | C2 | semidirect |
| 4. #20292601 | C2 | semidirect |
| 5. #20292600 | C2 | semidirect |
| 6. #20292585 | C2 | semidirect |
| 7. #421×C107 | C2 | semidirect |
| 13. C2×#13133808 | C4 | semidirect |
| 14. C2×#13133806 | C4 | semidirect |
| 15. C2×#13133805 | C4 | semidirect |
| 16. C2×#13133803 | C4 | semidirect |
| 133. C107 | #1976 | semidirect |
| 137. #421 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812129 | 2 |
| #20292663 | 2 |
| #20292643 | 2 |
| #20292601 | 2 |
| #20292600 | 2 |
| #20292585 | 2 |
| #421×C107 | 2 |
| #1976 | 107 |