Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×#16812054 | C2 | semidirect |
| 2. C2×#16812053 | C2 | semidirect |
| 4. #20292721 | C2 | semidirect |
| 5. Dic107⋊C16 | C2 | semidirect |
| 6. #20292427 | C2 | semidirect |
| 7. #357×C107 | C2 | semidirect |
| 26. Dic428 | D4 | semidirect |
| 71. Dic107 | SD32 | semidirect |
| 78. C107 | #2207 | semidirect |
| 85. #357 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812054 | 2 |
| C2×#16812053 | 2 |
| #20293002 | 2 |
| #20292721 | 2 |
| Dic107⋊C16 | 2 |
| #20292427 | 2 |
| #357×C107 | 2 |
| #2207 | 107 |