Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
174 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 174 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×#10587529 | C2 | semidirect |
| 2. C4⋊#63216 | C2 | semidirect |
| 3. #11763704 | C2 | semidirect |
| 4. C4×#63216 | C2 | semidirect |
| 27. #63216 | D4 | semidirect |
| 33. D68 | C16 | semidirect |
| 44. C2×D17 | C2×C16 | semidirect |
| 46. C4×C17 | C2×C16 | semidirect |
| 68. C17 | D4×C16 | semidirect |
| 100. C4 | #10587529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587529 | 2 |
| C4⋊#63216 | 2 |
| #11763704 | 2 |
| C4×#63216 | 2 |
| #11762874 | 2 |
| D4×C16 | 17 |