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×#17984135 | C2 | semidirect |
| 2. C2×#17984121 | C2 | semidirect |
| 3. C2×#17984108 | C2 | semidirect |
| 4. #22577984 | C2 | semidirect |
| 5. #22577566 | C2 | semidirect |
| 6. #22577560 | C2 | semidirect |
| 7. #22577549 | C2 | semidirect |
| 8. #22577543 | C2 | semidirect |
| 9. C2×#17984011 | C2 | semidirect |
| 10. #22577371 | C2 | semidirect |
| 11. #417×C137 | C2 | semidirect |
| 58. C2×Dic274 | D4 | semidirect |
| 87. #41×C137 | D4 | semidirect |
| 169. C137 | #3013 | semidirect |
| 179. #417 | D137 | semidirect |
| 224. #41 | D548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984135 | 2 |
| C2×#17984121 | 2 |
| C2×#17984108 | 2 |
| #22577984 | 2 |
| #22577566 | 2 |
| #22577560 | 2 |
| #22577549 | 2 |
| #22577543 | 2 |
| C2×#17984011 | 2 |
| #22577371 | 2 |
| #417×C137 | 2 |
| #3013 | 137 |