Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1160 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 210 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. C22×C22⋊#595 | C2 | semidirect |
| 2. #11763757 | C2 | semidirect |
| 3. #11763752 | C2 | semidirect |
| 4. #11763750 | C2 | semidirect |
| 8. C23×#595 | C22 | semidirect |
| 9. C22×D4×C17 | C4 | semidirect |
| 10. C22×C22⋊D17 | C4 | semidirect |
| 11. C22×C22⋊D17 | C4 | semidirect |
| 13. C2×D4×D17 | C4 | semidirect |
| 15. C22×D68 | C4 | semidirect |
| 19. C2×C22⋊#595 | C22 | semidirect |
| 20. C2×C22⋊#595 | C22 | semidirect |
| 21. (C2×#595)⋊C4 | C22 | semidirect |
| 23. C24×C17 | C2×C4 | semidirect |
| 29. C23×D17 | C2×C4 | semidirect |
| 30. C23×D17 | C2×C4 | semidirect |
| 39. C2×D4×C17 | C2×C4 | semidirect |
| 40. C22×C4×C17 | C2×C4 | semidirect |
| 43. C2×C22⋊D17 | C2×C4 | semidirect |
| 44. C2×C22⋊D17 | C2×C4 | semidirect |
| 45. C22×Dic17 | C2×C4 | semidirect |
| 50. C2×D68 | C2×C4 | semidirect |
| 52. C2×C4×D17 | C2×C4 | semidirect |
| 60. C23×C17 | C22⋊C4 | semidirect |
| 76. C22×D17 | C22⋊C4 | semidirect |
| 77. C22×D17 | C22⋊C4 | semidirect |
| 149. C22×D4 | #595 | semidirect |
| 157. C17 | #2308 | semidirect |
| 170. C24 | C2×#595 | semidirect |
| 181. C2×D4 | C2×#595 | semidirect |
| 189. C22×C4 | C2×#595 | semidirect |
| 217. C23 | C22⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#595 | 2 |
| #11763757 | 2 |
| #11763752 | 2 |
| #11763750 | 2 |
| C22×D4×D17 | 2 |
| #2308 | 17 |