Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 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×#10587471 | C2 | semidirect |
| 2. #11763084 | C2 | semidirect |
| 4. #11762639 | C2 | semidirect |
| 5. #11762626 | C2 | semidirect |
| 6. #11762623 | C2 | semidirect |
| 7. C17×#504 | C2 | semidirect |
| 69. #504 | D17 | semidirect |
| 94. C17 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587471 | 2 |
| #11763084 | 2 |
| #11763079 | 2 |
| #11762639 | 2 |
| #11762626 | 2 |
| #11762623 | 2 |
| C17×#504 | 2 |
| #2223 | 17 |