Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
880 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10587505 | C2 | semidirect |
| 2. #11762665 | C2 | semidirect |
| 4. C25×C17 | C4 | semidirect |
| 8. C22×D4×C17 | C4 | semidirect |
| 10. C23×C4×C17 | C4 | semidirect |
| 12. C2×C22⋊Dic17 | C22 | semidirect |
| 55. C23×C17 | C22⋊C4 | semidirect |
| 64. C2×C4×C17 | C22⋊C4 | semidirect |
| 83. C22×C17 | #99 | semidirect |
| 99. C25 | Dic17 | semidirect |
| 103. C22×D4 | Dic17 | semidirect |
| 105. C23×C4 | Dic17 | semidirect |
| 109. C17 | #1781 | semidirect |
| 151. C23 | C22⋊Dic17 | semidirect |
| 162. C2×C4 | C22⋊Dic17 | semidirect |
| 178. C22 | #10587505 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587505 | 2 |
| #11762665 | 2 |
| C23×D4×C17 | 2 |
| #1781 | 17 |