Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
400 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 199 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×#17984185 | C2 | semidirect |
| 2. #22578522 | C2 | direct (N × H) |
| 3. C2×#17984184 | C2 | semidirect |
| 4. C2×#17984183 | C2 | semidirect |
| 6. #17984185 | C22 | semidirect |
| 7. #17984184 | C22 | semidirect |
| 8. #17984183 | C22 | semidirect |
| 9. C2×#14555522 | C22 | semidirect |
| 19. #14555522 | C23 | semidirect |
| 70. C2×D137 | M32 | semidirect |
| 79. C2×C137 | C2×M32 | semidirect |
| 82. D137 | C2×M32 | semidirect |
| 83. C137 | C22×M32 | semidirect |
| 165. C2 | #22578522 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984185 | 2 |
| #22578522 | 2 |
| C2×#17984184 | 2 |
| C2×#17984183 | 2 |
| C22×#14555518 | 2 |
| C22×M32 | 137 |