Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
138 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 1. #11763210 | C2 | semidirect |
| 3. #11762613 | C2 | semidirect |
| 6. C16×Dic17 | C2 | semidirect |
| 7. C17×#358 | C2 | semidirect |
| 66. #358 | D17 | semidirect |
| 85. C17 | #2242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763210 | 2 |
| #11763194 | 2 |
| #11762613 | 2 |
| #11762611 | 2 |
| #11762609 | 2 |
| C16×Dic17 | 2 |
| C17×#358 | 2 |
| #2242 | 17 |