Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10587615 | C2 | semidirect |
| 3. #11762744 | C2 | semidirect |
| 4. #11762710 | C2 | semidirect |
| 5. #11762678 | C2 | semidirect |
| 6. C4×C22⋊Dic17 | C2 | semidirect |
| 7. C22×C4⋊C4×C17 | C2 | semidirect |
| 41. C22⋊Dic17 | D4 | semidirect |
| 86. C4×C17 | #123 | semidirect |
| 91. C22×C4⋊C4 | D17 | semidirect |
| 118. C17 | #2501 | semidirect |
| 182. C4 | #10587615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587615 | 2 |
| C2×#10587616 | 2 |
| #11762744 | 2 |
| #11762710 | 2 |
| #11762678 | 2 |
| C4×C22⋊Dic17 | 2 |
| C22×C4⋊C4×C17 | 2 |
| #2501 | 17 |