Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 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 |
|---|---|---|
| 2. C2×#16812052 | C2 | semidirect |
| 3. #20292427 | C2 | semidirect |
| 4. C22⋊(C107⋊C16) | C2 | semidirect |
| 5. #467×C107 | C2 | semidirect |
| 11. C2×C107⋊C16 | C22 | semidirect |
| 12. C2×Q16×C107 | C22 | semidirect |
| 15. #107×C107 | C22 | semidirect |
| 55. C22×C107 | SD32 | semidirect |
| 72. C107 | #2187 | semidirect |
| 75. #467 | D107 | semidirect |
| 79. C2×Q16 | C2×D107 | semidirect |
| 87. #107 | C2×D107 | semidirect |
| 131. C22 | #16812052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D856 | 2 |
| C2×#16812052 | 2 |
| #20292427 | 2 |
| C22⋊(C107⋊C16) | 2 |
| #467×C107 | 2 |
| #2187 | 107 |