Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×Q16×D107 | C2 | semidirect |
| 3. #20293069 | C2 | direct (N × H) |
| 4. C2×#16812055 | C2 | semidirect |
| 5. C2×#16812054 | C2 | semidirect |
| 6. C2×#16812052 | C2 | semidirect |
| 7. C2×#16812048 | C2 | semidirect |
| 8. C2×Q32×C107 | C2 | semidirect |
| 16. Q16×D107 | C22 | semidirect |
| 20. #16812055 | C22 | semidirect |
| 21. #16812054 | C22 | semidirect |
| 22. #16812052 | C22 | semidirect |
| 23. #16812048 | C22 | semidirect |
| 27. Q32×C107 | C22 | semidirect |
| 93. C2×C107 | #510 | semidirect |
| 98. C107 | C2×#510 | semidirect |
| 103. C2×Q32 | D107 | semidirect |
| 121. Q32 | C2×D107 | semidirect |
| 193. C2 | #20293069 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812132 | 2 |
| C2×Q16×D107 | 2 |
| #20293069 | 2 |
| C2×#16812055 | 2 |
| C2×#16812054 | 2 |
| C2×#16812052 | 2 |
| C2×#16812048 | 2 |
| C2×Q32×C107 | 2 |
| C2×#510 | 107 |