Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
438 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 101 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×#10587579 | C2 | semidirect |
| 3. C2×#10587480 | C2 | semidirect |
| 4. C2×#10587480 | C2 | semidirect |
| 5. #11762710 | C2 | semidirect |
| 6. #11762563 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 21. C2×D136 | C4 | semidirect |
| 42. C2×D68 | C2×C4 | semidirect |
| 50. C2×C8×C17 | C2×C4 | semidirect |
| 96. C2×Dic17 | D8 | semidirect |
| 104. D68 | C22⋊C4 | semidirect |
| 143. #340 | D17 | semidirect |
| 172. C17 | #1879 | semidirect |
| 201. C2×C8 | C4×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D136 | 2 |
| C2×#10587579 | 2 |
| C2×#10587480 | 2 |
| #11762710 | 2 |
| #11762563 | 2 |
| C17×#340 | 2 |
| #1879 | 17 |