Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
436 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 98 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×#10587547 | C2 | semidirect |
| 2. C4×#63242 | C2 | semidirect |
| 3. #11763755 | C2 | semidirect |
| 10. C17×#127 | C4 | semidirect |
| 12. #10587626 | C4 | semidirect |
| 13. #10587560 | C4 | semidirect |
| 35. #63242 | D4 | semidirect |
| 77. C4×C17 | #102 | semidirect |
| 79. Dic17 | #102 | semidirect |
| 98. #127 | #595 | semidirect |
| 104. C17 | #1957 | semidirect |
| 166. C4 | #10587547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587547 | 2 |
| C4×#63242 | 2 |
| #11763755 | 2 |
| #127×D17 | 2 |
| #1957 | 17 |