Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#10587471 | C2 | semidirect |
| 2. C2×#10587498 | C2 | semidirect |
| 3. C2×#10587499 | C2 | semidirect |
| 4. #11763187 | C2 | semidirect |
| 6. C16×Dic17 | C2 | semidirect |
| 7. C2×C17×SD32 | C2 | semidirect |
| 42. C16×C17 | D4 | semidirect |
| 43. #63214 | D4 | semidirect |
| 72. Dic17 | SD32 | semidirect |
| 76. C2×SD32 | D17 | semidirect |
| 99. C17 | #2248 | semidirect |
| 120. C16 | C22⋊D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587471 | 2 |
| C2×#10587498 | 2 |
| C2×#10587499 | 2 |
| #11763187 | 2 |
| #11763184 | 2 |
| C16×Dic17 | 2 |
| C2×C17×SD32 | 2 |
| #2248 | 17 |