Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1360 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 274 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. C22×C4⋊#595 | C2 | semidirect |
| 2. C22×C22⋊#595 | C2 | semidirect |
| 3. C22×C4×#595 | C2 | semidirect |
| 4. #11763761 | C2 | direct (N × H) |
| 9. C22×D4×C17 | C4 | semidirect |
| 10. C22×C22⋊D17 | C4 | semidirect |
| 13. C2×D4×D17 | C4 | semidirect |
| 15. C22×D68 | C4 | semidirect |
| 18. C2×C22⋊#595 | C22 | semidirect |
| 20. C2×C4⋊#595 | C22 | semidirect |
| 22. C2×C4×#595 | C22 | semidirect |
| 36. C22×#595 | D4 | semidirect |
| 40. C2×D4×C17 | C2×C4 | semidirect |
| 43. C2×C22⋊D17 | C2×C4 | semidirect |
| 49. C2×D68 | C2×C4 | semidirect |
| 85. C2×#595 | C2×D4 | semidirect |
| 87. C2×C4×C17 | C22⋊C4 | semidirect |
| 90. C2×Dic17 | C22⋊C4 | semidirect |
| 93. C4×D17 | C22⋊C4 | semidirect |
| 121. C4×C17 | C2×C22⋊C4 | semidirect |
| 122. Dic17 | C2×C22⋊C4 | semidirect |
| 129. C2×C17 | #390 | semidirect |
| 133. D17 | #390 | semidirect |
| 144. C22×D4 | #595 | semidirect |
| 154. C17 | C2×#390 | semidirect |
| 172. C2×D4 | C2×#595 | semidirect |
| 226. C2×C4 | C22⋊#595 | semidirect |
| 253. C4 | C2×C22⋊#595 | semidirect |
| 260. C2 | #11763761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#595 | 2 |
| C22×C22⋊#595 | 2 |
| C22×C4×#595 | 2 |
| #11763761 | 2 |
| C22×D4×D17 | 2 |
| C2×#390 | 17 |