Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
164 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 51 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×C16×D107 | C2 | semidirect |
| 3. #20292869 | C2 | semidirect |
| 5. #20292430 | C2 | semidirect |
| 6. #20292427 | C2 | semidirect |
| 7. #367×C107 | C2 | semidirect |
| 39. C16×C107 | D4 | semidirect |
| 63. C2×D107 | SD32 | semidirect |
| 76. C107 | #2217 | semidirect |
| 81. #367 | D107 | semidirect |
| 115. C16 | D428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812054 | 2 |
| C2×C16×D107 | 2 |
| #20292869 | 2 |
| #20292864 | 2 |
| #20292430 | 2 |
| #20292427 | 2 |
| #367×C107 | 2 |
| #2217 | 107 |