Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
852 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 153 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×C22⋊#3622 | C2 | semidirect |
| 3. C2×#10587491 | C2 | semidirect |
| 4. C2×C17×C22⋊C8 | C2 | semidirect |
| 13. C22×C8×C17 | C22 | semidirect |
| 14. C22×#3622 | C22 | semidirect |
| 23. C23×D17 | C8 | semidirect |
| 85. C22×C17 | C22⋊C8 | semidirect |
| 98. C2×D17 | C22⋊C8 | semidirect |
| 106. C2×C22⋊C8 | D17 | semidirect |
| 123. C22×C8 | C2×D17 | semidirect |
| 127. C17 | #1779 | semidirect |
| 202. C22 | #10587491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D17 | 2 |
| C2×C22⋊#3622 | 2 |
| C2×#10587491 | 2 |
| C2×C17×C22⋊C8 | 2 |
| #1779 | 17 |