Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. C2×#10587542 | C2 | semidirect |
| 4. C2×C4×#3624 | C2 | semidirect |
| 5. #11763675 | C2 | semidirect |
| 6. #11763675 | C2 | semidirect |
| 11. C2×#63247 | C4 | semidirect |
| 20. C22⋊#3624 | C4 | semidirect |
| 70. C2×C4×C17 | M16 | semidirect |
| 83. C2×Dic17 | M16 | semidirect |
| 93. #3624 | C22⋊C4 | semidirect |
| 150. C17 | #1753 | semidirect |
| 215. C2×C4 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63247 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×#10587542 | 2 |
| C2×C4×#3624 | 2 |
| #11763675 | 2 |
| C22⋊C4×Dic17 | 2 |
| #1753 | 17 |