Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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. C17×#107 | C4 | semidirect |
| 16. C17×#107 | C4 | semidirect |
| 17. C17×#106 | C4 | semidirect |
| 18. C17×#106 | C4 | semidirect |
| 103. #107 | Dic17 | semidirect |
| 104. #107 | Dic17 | semidirect |
| 105. #106 | Dic17 | semidirect |
| 106. #106 | Dic17 | semidirect |
| 111. C17 | #1922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11762836 | 2 |
| #11762765 | 2 |
| #11762574 | 2 |
| #11762568 | 2 |
| #11762563 | 2 |
| C17×#427 | 2 |
| #1922 | 17 |