Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×C4⋊#3622 | C2 | semidirect |
| 3. C2×#10587503 | C2 | semidirect |
| 4. C2×#10587480 | C2 | semidirect |
| 5. #11762711 | C2 | semidirect |
| 6. #11762571 | C2 | semidirect |
| 7. C17×#390 | C2 | semidirect |
| 88. C2×C4×C17 | D8 | semidirect |
| 139. #390 | D17 | semidirect |
| 167. C17 | #2054 | semidirect |
| 238. C2×C4 | #63228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63228 | 2 |
| C2×C4⋊#3622 | 2 |
| C2×#10587503 | 2 |
| C2×#10587480 | 2 |
| #11762711 | 2 |
| #11762571 | 2 |
| C17×#390 | 2 |
| #2054 | 17 |