Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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. #20292868 | C2 | semidirect |
| 4. #20292455 | C2 | semidirect |
| 5. #20292432 | C2 | semidirect |
| 6. #20292429 | C2 | semidirect |
| 7. C22×C16×C107 | C2 | semidirect |
| 39. C16×C107 | D4 | semidirect |
| 59. C22×C107 | SD32 | semidirect |
| 76. C107 | #2217 | semidirect |
| 78. C22×C16 | D107 | semidirect |
| 115. C16 | C22⋊D107 | semidirect |
| 138. C22 | #16812054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812054 | 2 |
| #20292868 | 2 |
| #20292863 | 2 |
| #20292455 | 2 |
| #20292432 | 2 |
| #20292429 | 2 |
| C22×C16×C107 | 2 |
| #2217 | 107 |