Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
340 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 105 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×#10587481 | C2 | semidirect |
| 4. C2×#10587486 | C2 | semidirect |
| 5. #11762714 | C2 | semidirect |
| 7. C2×C17×#107 | C2 | semidirect |
| 18. C2×#63219 | C4 | semidirect |
| 86. C8×C17 | C22⋊C4 | semidirect |
| 108. C2×#107 | D17 | semidirect |
| 136. C17 | #1973 | semidirect |
| 200. C8 | #63227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63219 | 2 |
| C2×#10587481 | 2 |
| C2×#10587480 | 2 |
| C2×#10587486 | 2 |
| #11762714 | 2 |
| #11762710 | 2 |
| C2×C17×#107 | 2 |
| #1973 | 17 |