Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 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. #22577162 | C2 | semidirect |
| 14. #117×C137 | C4 | semidirect |
| 16. C2×C4⋊C4×C137 | C4 | semidirect |
| 17. C2×C4⋊C4×C137 | C4 | semidirect |
| 91. C137 | #1826 | semidirect |
| 101. #117 | Dic137 | semidirect |
| 103. C2×C4⋊C4 | Dic137 | semidirect |
| 104. C2×C4⋊C4 | Dic137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577367 | 2 |
| C4×C22⋊Dic137 | 2 |
| #22577162 | 2 |
| C2×#117×C137 | 2 |
| #1826 | 137 |