Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
476 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 3. #20292670 | C2 | semidirect |
| 4. #20292667 | C2 | semidirect |
| 5. #20292663 | C2 | semidirect |
| 6. C2×#16812042 | C2 | semidirect |
| 8. #16812116 | C4 | semidirect |
| 26. #13133802 | C2×C4 | semidirect |
| 27. C2×C107⋊C8 | C2×C4 | semidirect |
| 77. C107 | #2913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812116 | 2 |
| #20293110 | 2 |
| #20292670 | 2 |
| #20292667 | 2 |
| #20292663 | 2 |
| C2×#16812042 | 2 |
| #520×C107 | 2 |
| #2913 | 107 |