Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#10587550 | C2 | semidirect |
| 2. C4×#63243 | C2 | semidirect |
| 3. C4×C4⋊#595 | C2 | semidirect |
| 9. C17×C4⋊Q8 | C4 | semidirect |
| 10. #10587633 | C4 | semidirect |
| 15. #10587560 | C4 | semidirect |
| 37. #63243 | D4 | semidirect |
| 82. C4×C17 | #104 | semidirect |
| 99. C4⋊Q8 | #595 | semidirect |
| 113. C17 | #1980 | semidirect |
| 177. C4 | #10587550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587550 | 2 |
| C4×#63243 | 2 |
| C4×C4⋊#595 | 2 |
| #11763360 | 2 |
| #1980 | 17 |