Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#17984114 | C2 | semidirect |
| 2. #22577953 | C2 | semidirect |
| 3. #22577618 | C2 | semidirect |
| 4. #22577608 | C2 | semidirect |
| 5. #22577598 | C2 | semidirect |
| 6. #22577427 | C2 | semidirect |
| 7. #22577402 | C2 | semidirect |
| 8. C2×C4×D4×C137 | C2 | semidirect |
| 14. #17984088 | C22 | semidirect |
| 15. #17984085 | C22 | semidirect |
| 16. #17984076 | C22 | semidirect |
| 21. C4⋊#11764040 | C22 | semidirect |
| 22. C4⋊#11764040 | C22 | semidirect |
| 23. #17984011 | C22 | semidirect |
| 24. #17984008 | C22 | semidirect |
| 53. C2×D4×C137 | D4 | semidirect |
| 119. C4×C137 | AGL(1,ℤ/8) | semidirect |
| 129. C137 | #3036 | semidirect |
| 133. C2×C4×D4 | D137 | semidirect |
| 174. C2×D4 | D548 | semidirect |
| 250. C4 | #17984114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984114 | 2 |
| #22577953 | 2 |
| #22577618 | 2 |
| #22577608 | 2 |
| #22577598 | 2 |
| #22577427 | 2 |
| #22577402 | 2 |
| C2×C4×D4×C137 | 2 |
| #3036 | 137 |