Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×Q16×D137 | C2 | semidirect |
| 3. #22577845 | C2 | direct (N × H) |
| 4. C2×#17984034 | C2 | semidirect |
| 5. C2×#17984033 | C2 | semidirect |
| 6. C2×#17984031 | C2 | semidirect |
| 7. C2×#17984027 | C2 | semidirect |
| 8. C2×Q32×C137 | C2 | semidirect |
| 16. Q16×D137 | C22 | semidirect |
| 20. #17984034 | C22 | semidirect |
| 21. #17984033 | C22 | semidirect |
| 22. #17984031 | C22 | semidirect |
| 23. #17984027 | C22 | semidirect |
| 27. Q32×C137 | C22 | semidirect |
| 93. C2×C137 | #510 | semidirect |
| 97. C137 | C2×#510 | semidirect |
| 103. C2×Q32 | D137 | semidirect |
| 121. Q32 | C2×D137 | semidirect |
| 193. C2 | #22577845 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984111 | 2 |
| C2×Q16×D137 | 2 |
| #22577845 | 2 |
| C2×#17984034 | 2 |
| C2×#17984033 | 2 |
| C2×#17984031 | 2 |
| C2×#17984027 | 2 |
| C2×Q32×C137 | 2 |
| C2×#510 | 137 |