Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
448 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22577700 | C2 | direct (N × H) |
| 3. C2×#17984021 | C2 | semidirect |
| 4. C2×#17984019 | C2 | semidirect |
| 5. C2×C4⋊#11764040 | C2 | semidirect |
| 8. C2×#125×C137 | C2 | semidirect |
| 17. #17984021 | C22 | semidirect |
| 18. #17984019 | C22 | semidirect |
| 19. C4⋊#11764040 | C22 | semidirect |
| 23. #125×C137 | C22 | semidirect |
| 98. C2×C137 | #478 | semidirect |
| 103. C137 | C2×#478 | semidirect |
| 105. C2×#125 | D137 | semidirect |
| 118. #125 | C2×D137 | semidirect |
| 203. C2 | #22577700 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D548 | 2 |
| #22577700 | 2 |
| C2×#17984021 | 2 |
| C2×#17984019 | 2 |
| C2×C4⋊#11764040 | 2 |
| C2×#17984008 | 2 |
| C2×#125×C137 | 2 |
| C2×#478 | 137 |