Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22577230 | C2 | semidirect |
| 3. #22577228 | C2 | semidirect |
| 4. #22577203 | C2 | semidirect |
| 5. #22577203 | C2 | semidirect |
| 6. C22⋊#14555485 | C2 | semidirect |
| 7. #427×C137 | C2 | semidirect |
| 69. C137 | #2234 | semidirect |
| 72. #427 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577639 | 2 |
| #22577230 | 2 |
| #22577228 | 2 |
| #22577203 | 2 |
| C22⋊#14555485 | 2 |
| #427×C137 | 2 |
| #2234 | 137 |