Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
332 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 10. C4×Q8×C17 | C4 | semidirect |
| 11. Q8×Dic17 | C4 | semidirect |
| 15. #10587573 | C4 | semidirect |
| 19. C4×Dic34 | C4 | semidirect |
| 20. #10587549 | C4 | direct (N × H) |
| 61. Q8×C17 | C42 | semidirect |
| 81. Dic34 | C42 | semidirect |
| 93. C4×C17 | #103 | semidirect |
| 99. Dic17 | #103 | semidirect |
| 118. C4×Q8 | #595 | semidirect |
| 129. C17 | C4×#103 | semidirect |
| 167. Q8 | C4×#595 | semidirect |
| 203. C4 | #10587549 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587549 | 2 |
| C4×#63242 | 2 |
| C4×C4⋊#595 | 2 |
| #11763682 | 2 |
| C4×Q8×D17 | 2 |
| C4×#103 | 17 |