Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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. C22×C8×D17 | C2 | semidirect |
| 3. C2×#10587492 | C2 | semidirect |
| 4. C2×#10587480 | C2 | semidirect |
| 5. #11762666 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 22. #10587581 | C4 | semidirect |
| 50. C2×C8×C17 | D4 | semidirect |
| 61. C2×#3622 | D4 | semidirect |
| 128. C2×D17 | #102 | semidirect |
| 143. #340 | D17 | semidirect |
| 171. C17 | #1893 | semidirect |
| 200. C2×C8 | D68 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D17 | 2 |
| C2×#10587581 | 2 |
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| #11762666 | 2 |
| #11762571 | 2 |
| C17×#340 | 2 |
| #1893 | 17 |