Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
436 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812108 | C2 | semidirect |
| 3. #20292985 | C2 | direct (N × H) |
| 4. C2×#16812034 | C2 | semidirect |
| 5. C2×#16812032 | C2 | semidirect |
| 7. C2×#16812019 | C2 | semidirect |
| 13. #16812108 | C22 | semidirect |
| 21. #16812034 | C22 | semidirect |
| 22. #16812032 | C22 | semidirect |
| 24. #16812019 | C22 | semidirect |
| 104. C2×C107 | #489 | semidirect |
| 109. C107 | C2×#489 | semidirect |
| 213. C2 | #20292985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812108 | 2 |
| C2×#16812096 | 2 |
| #20292985 | 2 |
| C2×#16812034 | 2 |
| C2×#16812032 | 2 |
| C2×#16812030 | 2 |
| C2×#16812019 | 2 |
| C2×#102×C107 | 2 |
| C2×#489 | 107 |