Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
226 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 57 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×Dic436 | C2 | semidirect |
| 2. C2×#16812644 | C2 | semidirect |
| 4. #20294831 | C2 | semidirect |
| 5. C22⋊C16×C109 | C2 | semidirect |
| 26. Dic436 | D4 | semidirect |
| 54. C22×C109 | SD32 | semidirect |
| 70. C109 | #2185 | semidirect |
| 75. C22⋊C16 | D109 | semidirect |
| 127. C22 | #16812644 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic436 | 2 |
| C2×#16812644 | 2 |
| #20295262 | 2 |
| #20294831 | 2 |
| C22⋊C16×C109 | 2 |
| #2185 | 109 |