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×Q8×D107 | C2 | semidirect |
| 2. #20293284 | C2 | direct (N × H) |
| 3. C2×#16812096 | C2 | semidirect |
| 4. C2×#16812088 | 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 |
| 11. C2×Q8×D107 | C22 | semidirect |
| 14. #16812096 | C22 | semidirect |
| 15. #16812088 | C22 | semidirect |
| 16. #16812080 | C22 | semidirect |
| 17. Q8×Dic107 | C22 | semidirect |
| 18. C4×C22⋊D107 | C22 | semidirect |
| 26. C2×#41×C107 | C22 | semidirect |
| 49. C2×Q8×C107 | D4 | semidirect |
| 64. C22×D107 | #41 | semidirect |
| 66. Q8×C107 | C2×D4 | semidirect |
| 93. C2×D107 | C2×#41 | semidirect |
| 100. C2×C107 | #548 | semidirect |
| 106. C107 | C2×#548 | semidirect |
| 107. C22×#41 | D107 | semidirect |
| 116. C2×#41 | C2×D107 | semidirect |
| 142. C2×Q8 | C22⋊D107 | semidirect |
| 173. Q8 | C2×C22⋊D107 | semidirect |
| 207. C2 | #20293284 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D107 | 2 |
| #20293284 | 2 |
| C2×#16812096 | 2 |
| C2×#16812088 | 2 |
| C2×#16812080 | 2 |
| C2×Q8×Dic107 | 2 |
| C2×C4×C22⋊D107 | 2 |
| C22×#41×C107 | 2 |
| C2×#548 | 107 |