Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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×#16812044 | C2 | semidirect |
| 3. C2×#16812036 | C2 | semidirect |
| 4. C2×#16812035 | C2 | semidirect |
| 5. #20292593 | C2 | semidirect |
| 6. C2×#16812019 | C2 | semidirect |
| 7. #408×C107 | C2 | semidirect |
| 11. C2×#13133808 | C4 | semidirect |
| 12. C2×#13133806 | C4 | semidirect |
| 13. C2×#13133805 | C4 | semidirect |
| 14. C2×#13133803 | C4 | semidirect |
| 120. C107 | #1975 | semidirect |
| 126. #408 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812129 | 2 |
| C2×#16812044 | 2 |
| C2×#16812036 | 2 |
| C2×#16812035 | 2 |
| #20292593 | 2 |
| C2×#16812019 | 2 |
| #408×C107 | 2 |
| #1975 | 107 |