Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #20293233 | C2 | direct (N × H) |
| 2. C2×#16812106 | C2 | semidirect |
| 3. C2×#16812094 | C2 | semidirect |
| 4. C2×#16812084 | C2 | semidirect |
| 5. C2×#16812084 | C2 | semidirect |
| 6. C2×#16812071 | C2 | semidirect |
| 7. C2×#16812066 | C2 | semidirect |
| 8. C2×#125×C107 | C2 | semidirect |
| 14. #16812106 | C22 | semidirect |
| 15. #16812094 | C22 | semidirect |
| 16. #16812084 | C22 | semidirect |
| 17. #16812084 | C22 | semidirect |
| 18. #16812071 | C22 | semidirect |
| 19. #16812066 | C22 | semidirect |
| 25. #125×C107 | C22 | semidirect |
| 92. C2×C107 | #540 | semidirect |
| 98. C107 | C2×#540 | semidirect |
| 101. C2×#125 | D107 | semidirect |
| 113. #125 | C2×D107 | semidirect |
| 192. C2 | #20293233 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293233 | 2 |
| C2×#16812106 | 2 |
| C2×#16812094 | 2 |
| C2×#16812084 | 2 |
| C2×#16812071 | 2 |
| C2×#16812066 | 2 |
| C2×#125×C107 | 2 |
| C2×#540 | 107 |