Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1232 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 274 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. C22×C4⋊#595 | C2 | semidirect |
| 4. #11763756 | C2 | direct (N × H) |
| 5. C2×(C2×#595)⋊C4 | C2 | semidirect |
| 18. C2×C4⋊#595 | C22 | semidirect |
| 19. C2×C22⋊C4×C17 | C4 | semidirect |
| 20. C2×C22⋊Dic17 | C4 | semidirect |
| 21. C2×#63227 | C4 | semidirect |
| 22. C22⋊C4×D17 | C4 | semidirect |
| 24. (C2×#595)⋊C4 | C22 | semidirect |
| 47. C22×C4×C17 | C2×C4 | semidirect |
| 48. C22×Dic17 | C2×C4 | semidirect |
| 51. C2×C4×D17 | C2×C4 | semidirect |
| 55. C22⋊C4×C17 | C2×C4 | semidirect |
| 56. C22⋊Dic17 | C2×C4 | semidirect |
| 57. #63227 | C2×C4 | semidirect |
| 59. C23×C17 | C4⋊C4 | semidirect |
| 69. C22×D17 | C4⋊C4 | semidirect |
| 70. C22×D17 | C4⋊C4 | semidirect |
| 92. C2×C4×C17 | C22×C4 | semidirect |
| 94. C2×Dic17 | C22×C4 | semidirect |
| 102. C22×C17 | C2×C4⋊C4 | semidirect |
| 112. C2×D17 | C2×C4⋊C4 | semidirect |
| 133. C2×C17 | #385 | semidirect |
| 137. D17 | #385 | semidirect |
| 157. C2×C22⋊C4 | #595 | semidirect |
| 159. C17 | C2×#385 | semidirect |
| 187. C22×C4 | C2×#595 | semidirect |
| 192. C22⋊C4 | C2×#595 | semidirect |
| 212. C23 | C4⋊#595 | semidirect |
| 232. C2×C4 | C22×#595 | semidirect |
| 252. C22 | C2×C4⋊#595 | semidirect |
| 266. C2 | #11763756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#595 | 2 |
| C22×C4⋊#595 | 2 |
| C22×C22⋊#595 | 2 |
| #11763756 | 2 |
| C2×(C2×#595)⋊C4 | 2 |
| C2×C22⋊C4×D17 | 2 |
| C2×#385 | 17 |