Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11762826 | C2 | semidirect |
| 2. #11762805 | C2 | semidirect |
| 3. #11762783 | C2 | semidirect |
| 4. #11762776 | C2 | semidirect |
| 7. C17×2−1+4 | C4 | semidirect |
| 10. C17×H(5,𝔽2) | C4 | semidirect |
| 15. #10587612 | C22 | semidirect |
| 16. C2×#63223 | C22 | semidirect |
| 17. C22×#3622 | C22 | semidirect |
| 115. 2−1+4 | Dic17 | semidirect |
| 118. H(5,𝔽2) | Dic17 | semidirect |
| 131. C17 | #1794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762826 | 2 |
| #11762805 | 2 |
| #11762783 | 2 |
| #11762776 | 2 |
| C17×#585 | 2 |
| #1794 | 17 |