Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
| 3. #20292974 | C2 | semidirect |
| 4. #20292918 | C2 | semidirect |
| 5. #20292828 | C2 | semidirect |
| 6. C4×#13133807 | C2 | semidirect |
| 7. C8×Q8×C107 | C2 | semidirect |
| 44. Q8×C107 | SD16 | semidirect |
| 58. Dic214 | #41 | semidirect |
| 77. C107 | #3362 | semidirect |
| 83. C8×Q8 | D107 | semidirect |
| 124. 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 |
| #20293299 | 2 |
| #20292974 | 2 |
| #20292918 | 2 |
| #20292828 | 2 |
| C4×#13133807 | 2 |
| C8×Q8×C107 | 2 |
| #3362 | 107 |