Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×#63218 | C2 | semidirect |
| 3. C2×C4⋊C4×D17 | C2 | semidirect |
| 4. #11762807 | C2 | direct (N × H) |
| 5. C2×#10587487 | C2 | semidirect |
| 6. C2×#10587481 | C2 | semidirect |
| 7. C2×#10587503 | C2 | semidirect |
| 8. C2×C17×#102 | C2 | semidirect |
| 14. C2×#63254 | C4 | semidirect |
| 25. C2×#63218 | C22 | semidirect |
| 27. C4⋊C4×D17 | C22 | semidirect |
| 28. C17×#102 | C22 | semidirect |
| 29. #10587503 | C22 | semidirect |
| 30. #10587487 | C22 | semidirect |
| 31. #10587481 | C22 | semidirect |
| 36. C2×D4×C17 | C2×C4 | semidirect |
| 49. #63254 | C2×C4 | semidirect |
| 58. C2×Dic34 | C2×C4 | semidirect |
| 81. D4×C17 | C22×C4 | semidirect |
| 102. Dic34 | C22×C4 | semidirect |
| 132. C2×#102 | D17 | semidirect |
| 134. C2×C17 | #417 | semidirect |
| 161. #102 | C2×D17 | semidirect |
| 162. C17 | C2×#417 | semidirect |
| 176. C2×D4 | C4×D17 | semidirect |
| 216. D4 | C2×C4×D17 | semidirect |
| 257. C2 | #11762807 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63254 | 2 |
| C22×#63218 | 2 |
| C2×C4⋊C4×D17 | 2 |
| #11762807 | 2 |
| C2×#10587487 | 2 |
| C2×#10587481 | 2 |
| C2×#10587503 | 2 |
| C2×C17×#102 | 2 |
| C2×#417 | 17 |