Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22577755 | C2 | semidirect |
| 3. #22577738 | C2 | semidirect |
| 4. #22577695 | C2 | semidirect |
| 5. #22577642 | C2 | semidirect |
| 6. #22577613 | C2 | semidirect |
| 7. #22577558 | C2 | semidirect |
| 8. C4×#14555500 | C2 | semidirect |
| 10. C2×#17984011 | C2 | semidirect |
| 92. D4×C137 | Q16 | semidirect |
| 122. C137 | #3299 | semidirect |
| 208. D4 | #14555500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic274 | 2 |
| #22577755 | 2 |
| #22577738 | 2 |
| #22577695 | 2 |
| #22577642 | 2 |
| #22577613 | 2 |
| #22577558 | 2 |
| C4×#14555500 | 2 |
| D4×#11764040 | 2 |
| C2×#17984011 | 2 |
| #554×C137 | 2 |
| #3299 | 137 |