Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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. #22578414 | C2 | semidirect |
| 3. #22578413 | C2 | semidirect |
| 4. C2×#17984157 | C2 | semidirect |
| 15. #17984096 | C4 | semidirect |
| 16. #17984095 | C4 | semidirect |
| 17. #17984094 | C4 | semidirect |
| 20. #131×C137 | C4 | semidirect |
| 33. #14555494 | C2×C4 | semidirect |
| 34. #14555493 | C2×C4 | semidirect |
| 35. C2×#11764040 | C2×C4 | semidirect |
| 36. C8×D137 | C2×C4 | semidirect |
| 37. C8×D137 | C2×C4 | semidirect |
| 41. M16×C137 | C2×C4 | semidirect |
| 42. C2×C8×C137 | C2×C4 | semidirect |
| 78. C137 | #2913 | semidirect |
| 89. #131 | #10587739 | semidirect |
| 110. M16 | C2×#10587739 | semidirect |
| 116. C2×C8 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578472 | 2 |
| #22578414 | 2 |
| #22578413 | 2 |
| C2×#17984157 | 2 |
| #131×D137 | 2 |
| #2913 | 137 |