Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#16812131 | C2 | semidirect |
| 2. #20293057 | C2 | direct (N × H) |
| 3. C2×#16812055 | C2 | semidirect |
| 4. C2×#16812053 | C2 | semidirect |
| 5. C2×#16812052 | C2 | semidirect |
| 6. C2×#16812050 | C2 | semidirect |
| 7. C22×C107⋊C16 | C2 | semidirect |
| 8. C2×#135×C107 | C2 | semidirect |
| 11. #16812131 | C22 | semidirect |
| 15. #16812055 | C22 | semidirect |
| 16. #16812053 | C22 | semidirect |
| 17. #16812052 | C22 | semidirect |
| 18. #16812050 | C22 | semidirect |
| 21. C2×C107⋊C16 | C22 | semidirect |
| 24. #135×C107 | C22 | semidirect |
| 96. C2×C107 | #508 | semidirect |
| 100. C107 | C2×#508 | semidirect |
| 102. C2×#135 | D107 | semidirect |
| 114. #135 | C2×D107 | semidirect |
| 197. C2 | #20293057 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293057 | 2 |
| C2×#16812055 | 2 |
| C2×#16812053 | 2 |
| C2×#16812052 | 2 |
| C2×#16812050 | 2 |
| C22×C107⋊C16 | 2 |
| C2×#135×C107 | 2 |
| C2×#508 | 107 |