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×#16812050 | C2 | semidirect |
| 2. C2×C16×D107 | C2 | semidirect |
| 3. #20292864 | C2 | semidirect |
| 4. #20292860 | C2 | semidirect |
| 5. #20292452 | C2 | semidirect |
| 6. #20292429 | C2 | semidirect |
| 7. #357×C107 | C2 | semidirect |
| 33. C107⋊C16 | D4 | semidirect |
| 67. C2×D107 | D16 | semidirect |
| 80. C107 | #2215 | semidirect |
| 87. #357 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812050 | 2 |
| C2×C16×D107 | 2 |
| #20292864 | 2 |
| #20292860 | 2 |
| #20292452 | 2 |
| #20292429 | 2 |
| #357×C107 | 2 |
| #2215 | 107 |