Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
338 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#17984006 | C2 | semidirect |
| 4. C2×#17984006 | C2 | semidirect |
| 6. #22577172 | C2 | semidirect |
| 7. #343×C137 | C2 | semidirect |
| 118. C2×D137 | #101 | semidirect |
| 134. C137 | #1901 | semidirect |
| 142. #343 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D137 | 2 |
| C2×#17984068 | 2 |
| C2×#17984006 | 2 |
| #22577366 | 2 |
| #22577172 | 2 |
| #343×C137 | 2 |
| #1901 | 137 |