Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 109 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×#10587485 | C2 | semidirect |
| 5. #11762678 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 20. #10587579 | C4 | semidirect |
| 89. D68 | C4⋊C4 | semidirect |
| 116. Dic17 | #102 | semidirect |
| 123. #340 | D17 | semidirect |
| 148. C17 | #1802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587579 | 2 |
| C2×#10587485 | 2 |
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| #11762678 | 2 |
| #11762571 | 2 |
| C17×#340 | 2 |
| #1802 | 17 |