Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20292669 | C2 | semidirect |
| 5. #20292496 | C2 | semidirect |
| 6. #20292388 | C2 | semidirect |
| 7. #343×C107 | C2 | semidirect |
| 20. #16812035 | C4 | semidirect |
| 48. C4×Dic107 | C2×C4 | semidirect |
| 54. M16×C107 | C2×C4 | semidirect |
| 80. D428 | C4⋊C4 | semidirect |
| 85. Dic214 | C4⋊C4 | semidirect |
| 113. C107 | #1859 | semidirect |
| 119. #343 | D107 | semidirect |
| 155. M16 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293108 | 2 |
| #20292669 | 2 |
| C2×#16812035 | 2 |
| #20292629 | 2 |
| #20292496 | 2 |
| #20292388 | 2 |
| #343×C107 | 2 |
| #1859 | 107 |