Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 3. C2×Q8×Dic137 | C2 | semidirect |
| 4. #22577627 | C2 | direct (N × H) |
| 5. C2×#17984017 | C2 | semidirect |
| 6. C2×#17984012 | C2 | semidirect |
| 8. C22×Q16×C137 | C2 | semidirect |
| 16. Q8×Dic137 | C22 | semidirect |
| 23. #17984017 | C22 | semidirect |
| 24. #17984012 | C22 | semidirect |
| 29. C2×Q16×C137 | C22 | semidirect |
| 110. C2×C137 | #464 | semidirect |
| 115. C137 | C2×#464 | semidirect |
| 117. C22×Q16 | D137 | semidirect |
| 129. C2×Q16 | C2×D137 | semidirect |
| 227. C2 | #22577627 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555497 | 2 |
| C2×#17984077 | 2 |
| C2×Q8×Dic137 | 2 |
| #22577627 | 2 |
| C2×#17984017 | 2 |
| C2×#17984012 | 2 |
| C2×#17984010 | 2 |
| C22×Q16×C137 | 2 |
| C2×#464 | 137 |