Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 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. #20293105 | C2 | semidirect |
| 3. #20293104 | C2 | semidirect |
| 4. #20293103 | C2 | semidirect |
| 5. C4×Q8×D107 | C2 | semidirect |
| 7. #519×C107 | C2 | semidirect |
| 9. C2×Q8×D107 | C4 | semidirect |
| 13. Q8×Dic107 | C22 | semidirect |
| 14. C4×Dic214 | C22 | semidirect |
| 15. #16812074 | C22 | semidirect |
| 24. C4×Q8×C107 | C22 | semidirect |
| 27. C2×Dic214 | C2×C4 | semidirect |
| 30. Q8×D107 | C2×C4 | semidirect |
| 42. C2×Q8×C107 | C2×C4 | semidirect |
| 80. D107 | #519 | direct (N × H) |
| 82. C107 | C2×#519 | semidirect |
| 87. #519 | D107 | direct (N × H) |
| 99. C4×Q8 | C2×D107 | semidirect |
| 113. C2×Q8 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D107 | 2 |
| #20293105 | 2 |
| #20293104 | 2 |
| #20293103 | 2 |
| C4×Q8×D107 | 2 |
| #117×D107 | 2 |
| #519×C107 | 2 |
| C2×#519 | 107 |