Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 15. C2×#63231 | C4 | semidirect |
| 127. C17 | #1979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63231 | 2 |
| C2×#10587493 | 2 |
| #11762817 | 2 |
| C2×#10587507 | 2 |
| C2×#10587495 | 2 |
| #11762765 | 2 |
| C17×#419 | 2 |
| #1979 | 17 |