Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×#10587489 | C2 | semidirect |
| 3. C2×#10587503 | C2 | semidirect |
| 4. C2×#10587491 | C2 | semidirect |
| 5. #11762666 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C2×C17×#102 | C2 | semidirect |
| 49. C2×C8×C17 | D4 | semidirect |
| 138. C2×#102 | D17 | semidirect |
| 168. C17 | #2033 | semidirect |
| 196. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587624 | 2 |
| C2×#10587489 | 2 |
| C2×#10587503 | 2 |
| C2×#10587491 | 2 |
| #11762666 | 2 |
| #11762571 | 2 |
| C2×C17×#102 | 2 |
| #2033 | 17 |