Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#17984016 | C2 | semidirect |
| 3. #22577405 | C2 | semidirect |
| 4. #22577404 | C2 | semidirect |
| 5. C2×#17984006 | C2 | semidirect |
| 6. #22577309 | C2 | semidirect |
| 7. C2×#104×C137 | C2 | semidirect |
| 11. #17984135 | C4 | semidirect |
| 154. C137 | #1793 | semidirect |
| 158. C2×#104 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984135 | 2 |
| C2×#17984016 | 2 |
| #22577405 | 2 |
| #22577404 | 2 |
| C2×#17984006 | 2 |
| #22577309 | 2 |
| C2×#104×C137 | 2 |
| #1793 | 137 |