Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. C2×#17984080 | C2 | semidirect |
| 3. #22577772 | C2 | semidirect |
| 4. #22577768 | C2 | semidirect |
| 5. #22577758 | C2 | semidirect |
| 6. #22577405 | C2 | semidirect |
| 7. C4×M16×C137 | C2 | semidirect |
| 77. C137 | #3142 | semidirect |
| 85. C4×M16 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577953 | 2 |
| C2×#17984080 | 2 |
| #22577772 | 2 |
| #22577768 | 2 |
| #22577758 | 2 |
| #22577405 | 2 |
| C4×M16×C137 | 2 |
| #3142 | 137 |