Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20293034 | C2 | semidirect |
| 3. #20293027 | C2 | semidirect |
| 4. #20293024 | C2 | semidirect |
| 29. #13133802 | Q8 | semidirect |
| 43. C2×C8×C107 | Q8 | semidirect |
| 76. C107 | #3163 | semidirect |
| 109. C2×C8 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293258 | 2 |
| #20293034 | 2 |
| #20293027 | 2 |
| #20293024 | 2 |
| #20292667 | 2 |
| #20292665 | 2 |
| #20292582 | 2 |
| C2×#106×C107 | 2 |
| #3163 | 107 |