Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
232 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. #20295876 | C2 | semidirect |
| 4. Q8⋊#11724786 | C2 | semidirect |
| 90. C109 | #1493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296029 | 2 |
| C2×C4×#11724786 | 2 |
| #20295876 | 2 |
| Q8⋊#11724786 | 2 |
| #20295578 | 2 |
| #1493 | 109 |