Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
144 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 62 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. #20295951 | C2 | semidirect |
| 4. #20295950 | C2 | semidirect |
| 14. #16812639 | C4 | semidirect |
| 16. C16×D109 | C4 | semidirect |
| 17. M32×C109 | C4 | semidirect |
| 63. C109 | #2155 | semidirect |
| 74. M32 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812769 | 2 |
| #20296036 | 2 |
| #20295951 | 2 |
| #20295950 | 2 |
| M32×D109 | 2 |
| #2155 | 109 |