Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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×#17984110 | C2 | semidirect |
| 2. C2×#17984108 | C2 | semidirect |
| 3. #22577949 | C2 | semidirect |
| 4. #22577796 | C2 | semidirect |
| 5. #22577794 | C2 | semidirect |
| 6. #22577791 | C2 | semidirect |
| 7. #22577789 | C2 | semidirect |
| 8. C2×#17983998 | C2 | semidirect |
| 9. C2×#135×C137 | C2 | semidirect |
| 51. C2×#11764040 | D4 | semidirect |
| 68. C2×C8×C137 | D4 | semidirect |
| 116. C137 | #3150 | semidirect |
| 120. C2×#135 | D137 | semidirect |
| 180. C2×C8 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984110 | 2 |
| C2×#17984108 | 2 |
| #22577949 | 2 |
| #22577796 | 2 |
| #22577794 | 2 |
| #22577791 | 2 |
| #22577789 | 2 |
| C2×#17983998 | 2 |
| C2×#135×C137 | 2 |
| #3150 | 137 |