Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
356 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
| 2. #20293021 | C2 | semidirect |
| 4. #20292850 | C2 | semidirect |
| 6. #20292838 | C2 | semidirect |
| 7. #20292729 | C2 | semidirect |
| 8. C4×Dic428 | C2 | semidirect |
| 9. #446×C107 | C2 | semidirect |
| 103. C107 | #3402 | semidirect |
| 110. #446 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293350 | 2 |
| #20293021 | 2 |
| #20293011 | 2 |
| #20292850 | 2 |
| #20292843 | 2 |
| #20292838 | 2 |
| #20292729 | 2 |
| C4×Dic428 | 2 |
| #446×C107 | 2 |
| #3402 | 107 |