Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 1. C2×#17984121 | C2 | semidirect |
| 3. #22577974 | C2 | semidirect |
| 4. #22577884 | C2 | semidirect |
| 5. #22577624 | C2 | semidirect |
| 6. #22577617 | C2 | semidirect |
| 7. #22577612 | C2 | semidirect |
| 8. #22577607 | C2 | semidirect |
| 9. #22577431 | C2 | semidirect |
| 10. C2×#17984011 | C2 | semidirect |
| 11. #417×C137 | C2 | semidirect |
| 146. C137 | #3046 | semidirect |
| 157. #417 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984121 | 2 |
| C2×#17984108 | 2 |
| #22577974 | 2 |
| #22577884 | 2 |
| #22577624 | 2 |
| #22577617 | 2 |
| #22577612 | 2 |
| #22577607 | 2 |
| #22577431 | 2 |
| C2×#17984011 | 2 |
| #417×C137 | 2 |
| #3046 | 137 |