Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
628 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 290 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 |
|---|---|---|
| 7. Q8×#595 | C4 | semidirect |
| 11. C4×Q8×C17 | C4 | semidirect |
| 12. Q8×Dic17 | C4 | semidirect |
| 14. #10587573 | C4 | semidirect |
| 16. C4×Dic34 | C4 | semidirect |
| 45. Q8×C17 | C42 | semidirect |
| 56. Dic34 | C42 | semidirect |
| 86. C4×Q8 | #595 | semidirect |
| 95. C17 | #2276 | semidirect |
| 116. Q8 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#595 | 2 |
| C4⋊C4×#595 | 2 |
| C4×C4⋊#595 | 2 |
| #11763745 | 2 |
| C4×Q8×D17 | 2 |
| #2276 | 17 |