Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20293432 | C2 | semidirect |
| 2. #20293068 | C2 | semidirect |
| 3. #20293062 | C2 | semidirect |
| 4. #20293057 | C2 | semidirect |
| 5. C2×#16812052 | C2 | semidirect |
| 6. #20293044 | C2 | semidirect |
| 7. #578×C107 | C2 | semidirect |
| 12. #16812055 | C22 | semidirect |
| 13. #16812053 | C22 | semidirect |
| 14. #16812052 | C22 | semidirect |
| 15. #16812052 | C22 | semidirect |
| 16. #16812050 | C22 | semidirect |
| 17. #16812049 | C22 | semidirect |
| 18. C2×C107⋊C16 | C22 | semidirect |
| 21. #135×C107 | C22 | semidirect |
| 22. C2×Q16×C107 | C22 | semidirect |
| 75. C107 | #3416 | semidirect |
| 76. #578 | D107 | semidirect |
| 88. #135 | C2×D107 | semidirect |
| 89. C2×Q16 | C2×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293432 | 2 |
| #20293068 | 2 |
| #20293062 | 2 |
| #20293057 | 2 |
| C2×#16812052 | 2 |
| #20293044 | 2 |
| #578×C107 | 2 |
| #3416 | 107 |