Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20293032 | C2 | semidirect |
| 4. #20292837 | C2 | semidirect |
| 5. #20292372 | C2 | semidirect |
| 7. Q8⋊C8×C107 | C2 | semidirect |
| 62. D428 | Q16 | semidirect |
| 93. C107 | #1649 | semidirect |
| 99. Q8⋊C8 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D428 | 2 |
| #20293032 | 2 |
| #20292908 | 2 |
| #20292837 | 2 |
| #20292372 | 2 |
| #20292356 | 2 |
| Q8⋊C8×C107 | 2 |
| #1649 | 107 |