Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
374 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 3. #11763756 | C2 | semidirect |
| 4. #11763686 | C2 | semidirect |
| 19. C17×#99 | C4 | semidirect |
| 20. #10587505 | C4 | semidirect |
| 21. #10587477 | C4 | semidirect |
| 49. C22⋊C4×C17 | C2×C4 | semidirect |
| 50. C22⋊Dic17 | C2×C4 | semidirect |
| 52. C23×C17 | C4⋊C4 | semidirect |
| 60. C22×D17 | C4⋊C4 | semidirect |
| 81. C2×C4×C17 | C4⋊C4 | semidirect |
| 85. C2×Dic17 | C4⋊C4 | semidirect |
| 146. #99 | #595 | semidirect |
| 149. C17 | #1867 | semidirect |
| 178. C22⋊C4 | C2×#595 | semidirect |
| 191. C23 | C4⋊#595 | semidirect |
| 218. C2×C4 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763876 | 2 |
| #11763757 | 2 |
| #11763756 | 2 |
| #11763686 | 2 |
| #99×D17 | 2 |
| #1867 | 17 |