Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1620 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1620 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. C22×Q8×D107 | C2 | semidirect |
| 3. #20293289 | C2 | direct (N × H) |
| 4. C2×#16812097 | C2 | semidirect |
| 5. C2×#16812089 | C2 | semidirect |
| 6. C2×#16812084 | C2 | semidirect |
| 7. C2×C4×D428 | C2 | semidirect |
| 8. C2×C4×Q8×C107 | C2 | semidirect |
| 10. C2×#13133819 | C22 | semidirect |
| 13. C2×Q8×D107 | C22 | semidirect |
| 18. #16812097 | C22 | semidirect |
| 19. #16812089 | C22 | semidirect |
| 20. #16812084 | C22 | semidirect |
| 21. C4×D428 | C22 | semidirect |
| 27. C4×Q8×C107 | C22 | semidirect |
| 50. C2×Q8×C107 | D4 | semidirect |
| 63. C22×D107 | #41 | semidirect |
| 66. Q8×C107 | C2×D4 | semidirect |
| 93. C2×D107 | C2×#41 | semidirect |
| 99. C2×C107 | #548 | semidirect |
| 106. C107 | C2×#548 | semidirect |
| 113. C2×C4×Q8 | D107 | semidirect |
| 128. C4×Q8 | C2×D107 | semidirect |
| 142. C2×Q8 | D428 | semidirect |
| 173. Q8 | C2×D428 | semidirect |
| 207. C2 | #20293289 | 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 |
| C22×Q8×D107 | 2 |
| #20293289 | 2 |
| C2×#16812097 | 2 |
| C2×#16812089 | 2 |
| C2×#16812084 | 2 |
| C2×C4×D428 | 2 |
| C2×C4×Q8×C107 | 2 |
| C2×#548 | 107 |