Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
752 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 269 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. #20295036 | C2 | direct (N × H) |
| 4. C2×#16812624 | C2 | semidirect |
| 9. C22×Dic218 | C4 | semidirect |
| 18. #16812624 | C22 | semidirect |
| 30. C2×Dic218 | C2×C4 | semidirect |
| 86. C2×C109 | #419 | semidirect |
| 90. C109 | C2×#419 | semidirect |
| 176. C2 | #20295036 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic218 | 2 |
| C2×#16812658 | 2 |
| #20295036 | 2 |
| C2×#16812624 | 2 |
| C22×M16×C109 | 2 |
| C2×#419 | 109 |