Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1736 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 573 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. C22×#13133819 | C2 | semidirect |
| 2. #20293296 | C2 | direct (N × H) |
| 3. C2×#16812105 | C2 | semidirect |
| 4. C2×#16812083 | C2 | semidirect |
| 5. C2×#16812080 | C2 | semidirect |
| 6. C2×Q8×Dic107 | C2 | semidirect |
| 7. C2×C4×C22⋊D107 | C2 | semidirect |
| 8. C22×#41×C107 | C2 | semidirect |
| 10. C2×#13133819 | C22 | semidirect |
| 15. #16812105 | C22 | semidirect |
| 16. #16812083 | C22 | semidirect |
| 17. #16812080 | C22 | semidirect |
| 18. Q8×Dic107 | C22 | semidirect |
| 19. C4×C22⋊D107 | C22 | semidirect |
| 26. C2×#41×C107 | C22 | semidirect |
| 50. C2×Q8×C107 | D4 | semidirect |
| 67. Q8×C107 | C2×D4 | semidirect |
| 78. C2×Dic107 | #41 | semidirect |
| 100. Dic107 | C2×#41 | semidirect |
| 102. C2×C107 | #550 | semidirect |
| 108. C107 | C2×#550 | semidirect |
| 110. C22×#41 | D107 | semidirect |
| 120. C2×#41 | C2×D107 | semidirect |
| 142. C2×Q8 | C22⋊D107 | semidirect |
| 175. Q8 | C2×C22⋊D107 | semidirect |
| 211. C2 | #20293296 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133819 | 2 |
| #20293296 | 2 |
| C2×#16812105 | 2 |
| C2×#16812083 | 2 |
| C2×#16812080 | 2 |
| C2×Q8×Dic107 | 2 |
| C2×C4×C22⋊D107 | 2 |
| C22×#41×C107 | 2 |
| C2×#550 | 107 |