Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20293350 | C2 | semidirect |
| 3. #20292974 | C2 | semidirect |
| 4. #20292954 | C2 | semidirect |
| 5. #20292912 | C2 | semidirect |
| 6. #20292859 | C2 | semidirect |
| 7. #20292827 | C2 | semidirect |
| 8. #20292788 | C2 | semidirect |
| 9. C8×D428 | C2 | semidirect |
| 10. #20292622 | C2 | semidirect |
| 11. C4×Q16×C107 | C2 | semidirect |
| 128. C107 | #3304 | semidirect |
| 137. C4×Q16 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293350 | 2 |
| #20293299 | 2 |
| #20292974 | 2 |
| #20292954 | 2 |
| #20292912 | 2 |
| #20292859 | 2 |
| #20292827 | 2 |
| #20292788 | 2 |
| C8×D428 | 2 |
| #20292622 | 2 |
| C4×Q16×C107 | 2 |
| #3304 | 107 |