Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
360 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 122 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. #11763675 | C2 | semidirect |
| 8. C22×#3624 | C4 | semidirect |
| 15. C22⋊#3624 | C4 | semidirect |
| 62. #3624 | C22⋊C4 | semidirect |
| 68. C22×C17 | #97 | semidirect |
| 103. C17 | #1752 | semidirect |
| 153. C22 | #10587542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3624 | 2 |
| C2×C22⋊#3624 | 2 |
| C2×#10587542 | 2 |
| #11763675 | 2 |
| C22⋊C4×Dic17 | 2 |
| #1752 | 17 |