Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587628 | C2 | semidirect |
| 3. #11762986 | C2 | direct (N × H) |
| 4. C2×#10587476 | C2 | semidirect |
| 5. C2×#10587504 | C2 | semidirect |
| 6. C2×C17×#124 | C2 | semidirect |
| 7. C22×Q8×C17 | C22 | semidirect |
| 17. C17×#124 | C22 | semidirect |
| 19. C2×C42×C17 | C22 | semidirect |
| 22. #10587628 | C22 | semidirect |
| 24. C2×#63223 | C22 | semidirect |
| 25. #10587504 | C22 | semidirect |
| 26. #10587476 | C22 | semidirect |
| 32. C2×Q8×C17 | C23 | semidirect |
| 58. C42×C17 | C23 | semidirect |
| 62. #63223 | C23 | semidirect |
| 116. C2×#124 | D17 | semidirect |
| 123. C2×C17 | #455 | semidirect |
| 131. C22×Q8 | C2×D17 | semidirect |
| 141. #124 | C2×D17 | semidirect |
| 143. C2×C42 | C2×D17 | semidirect |
| 146. C17 | C2×#455 | semidirect |
| 159. C2×Q8 | C22×D17 | semidirect |
| 183. C42 | C22×D17 | semidirect |
| 237. C2 | #11762986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587691 | 2 |
| C2×#10587628 | 2 |
| #11762986 | 2 |
| C2×#10587476 | 2 |
| C2×#10587504 | 2 |
| C2×C17×#124 | 2 |
| C2×#455 | 17 |