Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 1. C22×#13182038 | C2 | semidirect |
| 2. C23×#11724786 | C2 | semidirect |
| 3. #20295999 | C2 | direct (N × H) |
| 4. C2×#16812756 | C2 | semidirect |
| 5. C2×C22⋊#11724786 | C2 | semidirect |
| 8. C2×#13182038 | C22 | semidirect |
| 12. C22×#11724786 | C22 | semidirect |
| 13. #16812756 | C22 | semidirect |
| 14. C22⋊#11724786 | C22 | semidirect |
| 117. C2×C109 | #408 | semidirect |
| 122. C109 | C2×#408 | semidirect |
| 240. C2 | #20295999 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182038 | 2 |
| C23×#11724786 | 2 |
| #20295999 | 2 |
| C2×#16812756 | 2 |
| C2×C22⋊#11724786 | 2 |
| C22×#13182028 | 2 |
| C2×#408 | 109 |