Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#16812131 | C2 | semidirect |
| 2. #20293059 | C2 | direct (N × H) |
| 3. C2×Dic856 | C2 | semidirect |
| 4. C2×#16812054 | C2 | semidirect |
| 5. C2×D1712 | C2 | semidirect |
| 6. C22×C16×C107 | C2 | semidirect |
| 9. #16812131 | C22 | semidirect |
| 13. Dic856 | C22 | semidirect |
| 14. #16812054 | C22 | semidirect |
| 15. D1712 | C22 | semidirect |
| 19. C2×C16×C107 | C22 | semidirect |
| 64. C2×C107 | #508 | semidirect |
| 68. C107 | C2×#508 | semidirect |
| 74. C22×C16 | D107 | semidirect |
| 87. C2×C16 | C2×D107 | semidirect |
| 133. C2 | #20293059 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| #20293059 | 2 |
| C2×Dic856 | 2 |
| C2×#16812054 | 2 |
| C2×D1712 | 2 |
| C22×C16×C107 | 2 |
| C2×#508 | 107 |