Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 4. #20292397 | C2 | semidirect |
| 5. #20292387 | C2 | semidirect |
| 6. #20292383 | C2 | semidirect |
| 7. #533×C107 | C2 | semidirect |
| 27. C2×Dic214 | Q8 | semidirect |
| 28. C2×D428 | Q8 | semidirect |
| 102. C107 | #2031 | semidirect |
| 103. #533 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292645 | 2 |
| C2×#16812037 | 2 |
| #20292600 | 2 |
| #20292397 | 2 |
| #20292387 | 2 |
| #20292383 | 2 |
| #533×C107 | 2 |
| #2031 | 107 |