Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
344 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #11762572 | C2 | semidirect |
| 5. #11762571 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 19. C4⋊C4×D17 | C4 | semidirect |
| 120. #340 | D17 | semidirect |
| 143. C17 | #1823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D17 | 2 |
| C2×#10587491 | 2 |
| #11762666 | 2 |
| #11762572 | 2 |
| #11762571 | 2 |
| C17×#340 | 2 |
| #1823 | 17 |