Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984136 | C2 | semidirect |
| 2. C2×#17984108 | C2 | semidirect |
| 3. #22577981 | C2 | semidirect |
| 4. #22577564 | C2 | semidirect |
| 5. #22577557 | C2 | semidirect |
| 6. #22577547 | C2 | semidirect |
| 7. #22577540 | C2 | semidirect |
| 8. #22577405 | C2 | semidirect |
| 9. C2×#17984012 | C2 | semidirect |
| 10. #22577371 | C2 | semidirect |
| 11. C2×#137×C137 | C2 | semidirect |
| 52. #14555510 | D4 | semidirect |
| 86. C2×Q8×C137 | D4 | semidirect |
| 169. C137 | #3013 | semidirect |
| 172. C2×#137 | D137 | semidirect |
| 233. C2×Q8 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984136 | 2 |
| C2×#17984108 | 2 |
| #22577981 | 2 |
| #22577564 | 2 |
| #22577557 | 2 |
| #22577547 | 2 |
| #22577540 | 2 |
| #22577405 | 2 |
| C2×#17984012 | 2 |
| #22577371 | 2 |
| C2×#137×C137 | 2 |
| #3013 | 137 |