Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22577960 | C2 | semidirect |
| 3. #22577734 | C2 | semidirect |
| 4. #22577694 | C2 | semidirect |
| 5. #22577609 | C2 | semidirect |
| 7. C4×#14555499 | C2 | semidirect |
| 8. #431×C137 | C2 | semidirect |
| 12. #17984088 | C22 | semidirect |
| 13. #17984088 | C22 | semidirect |
| 18. C4×Dic274 | C22 | semidirect |
| 26. #17984020 | C22 | semidirect |
| 27. #17984013 | C22 | semidirect |
| 30. C4⋊C8×C137 | C22 | semidirect |
| 32. C4×C8×C137 | C22 | semidirect |
| 82. C2×C4×C137 | SD16 | semidirect |
| 112. C137 | #3101 | semidirect |
| 121. #431 | D137 | semidirect |
| 141. C4⋊C8 | C2×D137 | semidirect |
| 145. C4×C8 | C2×D137 | semidirect |
| 195. C2×C4 | #14555499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577960 | 2 |
| C2×C4×D548 | 2 |
| #22577734 | 2 |
| #22577694 | 2 |
| #22577609 | 2 |
| #22577556 | 2 |
| C4×#14555499 | 2 |
| #431×C137 | 2 |
| #3101 | 137 |