Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20292974 | C2 | semidirect |
| 3. #20292827 | C2 | semidirect |
| 5. #20292374 | C2 | semidirect |
| 6. #20292356 | C2 | semidirect |
| 7. Q8⋊C8×C107 | C2 | semidirect |
| 96. C107 | #1628 | semidirect |
| 102. Q8⋊C8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293350 | 2 |
| #20292974 | 2 |
| #20292827 | 2 |
| #20292823 | 2 |
| #20292374 | 2 |
| #20292356 | 2 |
| Q8⋊C8×C107 | 2 |
| #1628 | 107 |