Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16812028 | C2 | semidirect |
| 4. #20292396 | C2 | semidirect |
| 88. C22×C107 | #101 | semidirect |
| 105. C107 | #1901 | semidirect |
| 193. C22 | #16812028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133802 | 2 |
| C2×#16812028 | 2 |
| #20292591 | 2 |
| #20292396 | 2 |
| C2×C22⋊Q8×C107 | 2 |
| #1901 | 107 |