Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 10. #16812055 | C4 | semidirect |
| 64. C107 | #2176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812055 | 2 |
| C4×Dic428 | 2 |
| #20292454 | 2 |
| #20292431 | 2 |
| #20292430 | 2 |
| #20292403 | 2 |
| C4×Q16×C107 | 2 |
| #2176 | 107 |