Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #11762667 | C2 | semidirect |
| 4. #11762575 | C2 | semidirect |
| 7. C23×Dic17 | C4 | semidirect |
| 10. C2×C22⋊Dic17 | C4 | semidirect |
| 15. C2×C4⋊Dic17 | C4 | semidirect |
| 17. C2×C4×Dic17 | C4 | semidirect |
| 56. C23×C17 | C4⋊C4 | semidirect |
| 69. C2×C4×C17 | C4⋊C4 | semidirect |
| 111. Dic17 | #99 | semidirect |
| 140. C17 | #1799 | semidirect |
| 176. C23 | #63225 | semidirect |
| 205. C2×C4 | #63225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic17 | 2 |
| C2×#10587505 | 2 |
| #11762667 | 2 |
| #11762575 | 2 |
| C2×C17×#99 | 2 |
| #1799 | 17 |