Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#10587487 | C2 | semidirect |
| 3. C2×#10587481 | C2 | semidirect |
| 4. C2×#10587503 | C2 | semidirect |
| 5. C2×#10587491 | C2 | semidirect |
| 6. #11762666 | C2 | semidirect |
| 7. C2×C17×#102 | C2 | semidirect |
| 16. C2×#63254 | C4 | semidirect |
| 94. D4×C17 | C22⋊C4 | semidirect |
| 122. Dic34 | C22⋊C4 | semidirect |
| 159. C2×#102 | D17 | semidirect |
| 193. C17 | #1788 | semidirect |
| 263. D4 | #63227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63254 | 2 |
| C2×#10587487 | 2 |
| C2×#10587481 | 2 |
| C2×#10587503 | 2 |
| C2×#10587491 | 2 |
| #11762666 | 2 |
| C2×C17×#102 | 2 |
| #1788 | 17 |