Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
324 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 98 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. Q8×#595 | C4 | semidirect |
| 20. #10587549 | C4 | semidirect |
| 23. C17×#103 | C4 | semidirect |
| 24. #10587506 | C4 | semidirect |
| 25. #10587487 | C4 | semidirect |
| 26. #10587481 | C4 | semidirect |
| 74. Q8×C17 | C42 | semidirect |
| 92. Dic34 | C42 | semidirect |
| 146. #103 | #595 | semidirect |
| 149. C17 | #1763 | semidirect |
| 189. 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 |
| C2×#10587549 | 2 |
| C2×#10587532 | 2 |
| C4⋊C4×#595 | 2 |
| #11763683 | 2 |
| #11763682 | 2 |
| #103×D17 | 2 |
| #1763 | 17 |