Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
230 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 81 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. #11762836 | C2 | semidirect |
| 4. C2×C8×Dic17 | C2 | semidirect |
| 5. #11762574 | C2 | semidirect |
| 6. #11762568 | C2 | semidirect |
| 15. C17×#103 | C4 | semidirect |
| 16. C17×#102 | C4 | semidirect |
| 107. #103 | Dic17 | semidirect |
| 108. #102 | Dic17 | semidirect |
| 111. C17 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762836 | 2 |
| C2×#10587508 | 2 |
| #11762776 | 2 |
| C2×C8×Dic17 | 2 |
| #11762574 | 2 |
| #11762568 | 2 |
| C17×#416 | 2 |
| #1937 | 17 |