Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #11763287 | C2 | semidirect |
| 3. #11762818 | C2 | semidirect |
| 5. #11762580 | C2 | semidirect |
| 6. #11762566 | C2 | semidirect |
| 12. C2×Q16×C17 | C4 | semidirect |
| 13. C2×SD16×C17 | C4 | semidirect |
| 121. C2×Q16 | Dic17 | semidirect |
| 122. C2×SD16 | Dic17 | semidirect |
| 134. C17 | #1905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763287 | 2 |
| #11762826 | 2 |
| #11762818 | 2 |
| #11762783 | 2 |
| #11762580 | 2 |
| #11762566 | 2 |
| C2×C17×#137 | 2 |
| #1905 | 17 |