Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #11763609 | C2 | semidirect |
| 2. C2×#10587618 | C2 | semidirect |
| 3. #11763376 | C2 | semidirect |
| 4. #11762827 | C2 | semidirect |
| 5. #11762782 | C2 | semidirect |
| 6. #11762580 | C2 | semidirect |
| 7. C17×#418 | C2 | semidirect |
| 51. C2×D68 | D4 | semidirect |
| 55. C2×Dic34 | D4 | semidirect |
| 58. C2×C8×C17 | D4 | semidirect |
| 69. #63223 | D4 | semidirect |
| 140. #418 | D17 | semidirect |
| 173. C17 | #2008 | semidirect |
| 210. C2×C8 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763609 | 2 |
| C2×#10587618 | 2 |
| #11763376 | 2 |
| #11762827 | 2 |
| #11762782 | 2 |
| #11762580 | 2 |
| C17×#418 | 2 |
| #2008 | 17 |