Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 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 |
|---|---|---|
| 1. Q8×Dic214 | C2 | semidirect |
| 5. #20292375 | C2 | semidirect |
| 6. #20292359 | C2 | semidirect |
| 7. Q8⋊C8×C107 | C2 | semidirect |
| 52. Q8×C107 | SD16 | semidirect |
| 69. Dic214 | SD16 | semidirect |
| 92. C107 | #1623 | semidirect |
| 99. Q8⋊C8 | D107 | semidirect |
| 148. Q8 | #13133807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic214 | 2 |
| #20293000 | 2 |
| #20292828 | 2 |
| #20292827 | 2 |
| #20292375 | 2 |
| #20292359 | 2 |
| Q8⋊C8×C107 | 2 |
| #1623 | 107 |