Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 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×M16×D17 | C2 | semidirect |
| 3. C2×#10587504 | C2 | semidirect |
| 4. C2×#10587494 | C2 | semidirect |
| 5. #100×D17 | C2 | direct (N × H) |
| 6. C2×C17×#100 | C2 | semidirect |
| 17. C2×M16×C17 | C22 | semidirect |
| 18. C2×#63223 | C22 | semidirect |
| 20. M16×D17 | C22 | semidirect |
| 23. C17×#100 | C22 | semidirect |
| 24. #10587504 | C22 | semidirect |
| 25. #10587494 | C22 | semidirect |
| 57. M16×C17 | C23 | semidirect |
| 60. #63223 | C23 | semidirect |
| 120. C2×D17 | #100 | direct (N × H) |
| 131. C2×#100 | D17 | direct (N × H) |
| 135. C2×C17 | C2×#100 | semidirect |
| 139. D17 | C2×#100 | direct (N × H) |
| 154. C2×M16 | C2×D17 | semidirect |
| 158. #100 | C2×D17 | direct (N × H) |
| 159. C17 | C22×#100 | semidirect |
| 194. M16 | C22×D17 | semidirect |
| 265. C2 | #100×D17 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D17 | 2 |
| C2×M16×D17 | 2 |
| C2×#10587504 | 2 |
| C2×#10587494 | 2 |
| #100×D17 | 2 |
| C2×C17×#100 | 2 |
| C22×#100 | 17 |