Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
368 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 213 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. #20293043 | C2 | direct (N × H) |
| 3. C2×#16812049 | C2 | semidirect |
| 4. C2×#16812048 | C2 | semidirect |
| 5. C2×C16×D107 | C2 | semidirect |
| 6. C22×C16×C107 | C2 | semidirect |
| 13. #16812049 | C22 | semidirect |
| 14. #16812048 | C22 | semidirect |
| 16. C16×D107 | C22 | semidirect |
| 20. C2×C16×C107 | C22 | semidirect |
| 66. C2×C107 | #504 | semidirect |
| 70. C107 | C2×#504 | semidirect |
| 76. C22×C16 | D107 | semidirect |
| 90. C2×C16 | C2×D107 | semidirect |
| 137. C2 | #20293043 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812115 | 2 |
| #20293043 | 2 |
| C2×#16812049 | 2 |
| C2×#16812048 | 2 |
| C2×C16×D107 | 2 |
| C22×C16×C107 | 2 |
| C2×#504 | 107 |