Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
192 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 71 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. #11762874 | C2 | semidirect |
| 3. #11762536 | C2 | semidirect |
| 4. #11762530 | C2 | semidirect |
| 5. C17×#334 | C2 | semidirect |
| 26. D136 | C8 | semidirect |
| 34. D68 | C2×C8 | semidirect |
| 39. C8×C17 | C2×C8 | semidirect |
| 54. #334 | D17 | semidirect |
| 71. C17 | #1580 | semidirect |
| 97. C8 | C8×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D136 | 2 |
| #11762874 | 2 |
| #11762536 | 2 |
| #11762530 | 2 |
| C17×#334 | 2 |
| #1580 | 17 |