Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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 |
|---|---|---|
| 7. C2×#63216 | C4 | semidirect |
| 12. C17×M32 | C4 | semidirect |
| 13. #10587483 | C4 | semidirect |
| 67. M32 | #595 | semidirect |
| 74. C17 | #1379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587529 | 2 |
| #11763772 | 2 |
| M32×D17 | 2 |
| #1379 | 17 |