Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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×#16812045 | C2 | semidirect |
| 3. C2×#16812037 | C2 | semidirect |
| 4. #20292593 | C2 | semidirect |
| 5. C2×C4×C8×C107 | C2 | semidirect |
| 9. C2×Dic428 | C4 | semidirect |
| 10. C2×#13133807 | C4 | semidirect |
| 11. C2×D856 | C4 | semidirect |
| 86. C107 | #1974 | semidirect |
| 91. C2×C4×C8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812131 | 2 |
| C2×#16812045 | 2 |
| C2×#16812037 | 2 |
| #20292593 | 2 |
| C2×C4×C8×C107 | 2 |
| #1974 | 107 |