Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11763899 | C2 | semidirect |
| 3. #11763898 | C2 | semidirect |
| 27. C2×C8×C17 | C8 | semidirect |
| 28. C2×#3622 | C8 | semidirect |
| 29. C8×D17 | C8 | semidirect |
| 30. C8×D17 | C8 | semidirect |
| 86. C17 | #1564 | semidirect |
| 100. C2×C8 | #3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763922 | 2 |
| #11763899 | 2 |
| #11763898 | 2 |
| C2×C8×#595 | 2 |
| #1564 | 17 |