Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 19. #10587474 | C4 | semidirect |
| 20. C4×#3622 | C4 | semidirect |
| 99. C17 | #1833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587493 | 2 |
| #11762845 | 2 |
| #11762765 | 2 |
| #11762581 | 2 |
| #11762579 | 2 |
| #11762565 | 2 |
| C17×H(3,ℤ/4) | 2 |
| #1833 | 17 |