Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#17984118 | C2 | semidirect |
| 2. C2×#17984095 | C2 | semidirect |
| 3. #22577974 | C2 | semidirect |
| 4. #22577659 | C2 | semidirect |
| 5. #22577647 | C2 | semidirect |
| 6. #22577642 | C2 | semidirect |
| 7. #22577630 | C2 | semidirect |
| 8. #22577443 | C2 | semidirect |
| 9. #22577399 | C2 | semidirect |
| 10. C2×#17984011 | C2 | semidirect |
| 51. #14555494 | D4 | semidirect |
| 143. C137 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984118 | 2 |
| C2×#17984095 | 2 |
| #22577974 | 2 |
| #22577659 | 2 |
| #22577647 | 2 |
| #22577642 | 2 |
| #22577630 | 2 |
| #22577443 | 2 |
| #22577399 | 2 |
| C2×#17984011 | 2 |
| #537×C137 | 2 |
| #3063 | 137 |