Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1104 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 210 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×#10587677 | C2 | semidirect |
| 2. #11763761 | C2 | semidirect |
| 3. #11763750 | C2 | semidirect |
| 6. C22×D4×C17 | C4 | semidirect |
| 7. C22×C22⋊D17 | C4 | semidirect |
| 9. C2×D4×D17 | C4 | semidirect |
| 11. C22×D68 | C4 | semidirect |
| 14. C2×C22⋊#595 | C22 | semidirect |
| 16. C2×C4⋊#595 | C22 | semidirect |
| 17. C2×C4×#595 | C22 | semidirect |
| 63. C2×C4×C17 | C22⋊C4 | semidirect |
| 66. C2×Dic17 | C22⋊C4 | semidirect |
| 69. C4×D17 | C22⋊C4 | semidirect |
| 109. C22×D4 | #595 | semidirect |
| 116. C17 | #2309 | semidirect |
| 169. C2×C4 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587677 | 2 |
| #11763761 | 2 |
| #11763750 | 2 |
| C22×D4×D17 | 2 |
| #2309 | 17 |