Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
252 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 77 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. #11762866 | C2 | semidirect |
| 2. #11762677 | C2 | semidirect |
| 3. #11762543 | C2 | semidirect |
| 6. C17×C4⋊Q8 | C4 | semidirect |
| 7. C17×#127 | C4 | semidirect |
| 12. C4×D4×C17 | C4 | semidirect |
| 88. C4⋊Q8 | Dic17 | semidirect |
| 89. #127 | Dic17 | semidirect |
| 94. C4×D4 | Dic17 | semidirect |
| 102. C17 | #1514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762866 | 2 |
| #11762677 | 2 |
| #11762543 | 2 |
| C17×#532 | 2 |
| #1514 | 17 |