Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#17984113 | C2 | semidirect |
| 2. C22×#14555497 | C2 | semidirect |
| 3. #22577967 | C2 | semidirect |
| 4. #22577548 | C2 | semidirect |
| 5. #22577542 | C2 | semidirect |
| 6. #22577412 | C2 | semidirect |
| 7. #22577399 | C2 | semidirect |
| 8. #22577370 | C2 | semidirect |
| 9. C2×2−1+4×C137 | C2 | semidirect |
| 23. #17984012 | C22 | semidirect |
| 24. #17984012 | C22 | semidirect |
| 25. #17984009 | C22 | semidirect |
| 26. C22⋊#11764040 | C22 | semidirect |
| 33. C2×#41×C137 | C22 | semidirect |
| 36. C22×Q8×C137 | C22 | semidirect |
| 61. #41×C137 | D4 | semidirect |
| 69. C2×Q8×C137 | D4 | semidirect |
| 145. C137 | #3010 | semidirect |
| 147. C2×2−1+4 | D137 | semidirect |
| 162. C2×#41 | C2×D137 | semidirect |
| 165. C22×Q8 | C2×D137 | semidirect |
| 191. #41 | C22⋊D137 | semidirect |
| 199. C2×Q8 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984113 | 2 |
| C22×#14555497 | 2 |
| #22577967 | 2 |
| #22577548 | 2 |
| #22577542 | 2 |
| #22577412 | 2 |
| #22577399 | 2 |
| #22577370 | 2 |
| C2×2−1+4×C137 | 2 |
| #3010 | 137 |