Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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. C22×#14555498 | C2 | semidirect |
| 2. C2×#17984096 | C2 | semidirect |
| 3. #22577979 | C2 | semidirect |
| 5. #22577648 | C2 | semidirect |
| 6. #22577631 | C2 | semidirect |
| 7. #22577439 | C2 | semidirect |
| 8. #22577413 | C2 | semidirect |
| 9. #418×C137 | C2 | semidirect |
| 16. C2×#14555493 | C22 | semidirect |
| 18. C2×C8×D137 | C22 | semidirect |
| 24. #17984068 | C22 | semidirect |
| 28. #17984021 | C22 | semidirect |
| 29. #17984019 | C22 | semidirect |
| 30. #17984013 | C22 | semidirect |
| 50. C2×#11764040 | D4 | semidirect |
| 120. C137 | #3057 | semidirect |
| 130. #418 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555498 | 2 |
| C2×#17984096 | 2 |
| #22577979 | 2 |
| #22577970 | 2 |
| #22577648 | 2 |
| #22577631 | 2 |
| #22577439 | 2 |
| #22577413 | 2 |
| #418×C137 | 2 |
| #3057 | 137 |