Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
680 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 365 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. C2×#10587474 | C2 | semidirect |
| 4. C2×#10587486 | C2 | semidirect |
| 5. #97×D17 | C2 | direct (N × H) |
| 6. C2×C17×#97 | C2 | semidirect |
| 14. C2×C8×D17 | C4 | semidirect |
| 18. C17×#97 | C22 | semidirect |
| 19. #10587486 | C22 | semidirect |
| 20. #10587474 | C22 | semidirect |
| 31. C2×C8×C17 | C2×C4 | semidirect |
| 38. C2×#3622 | C2×C4 | semidirect |
| 40. C8×D17 | C2×C4 | semidirect |
| 57. C8×C17 | C22×C4 | semidirect |
| 58. #3622 | C22×C4 | semidirect |
| 63. C2×D17 | #97 | direct (N × H) |
| 76. C2×#97 | D17 | direct (N × H) |
| 77. C2×C17 | C2×#97 | semidirect |
| 80. D17 | C2×#97 | direct (N × H) |
| 94. #97 | C2×D17 | direct (N × H) |
| 95. C17 | C22×#97 | semidirect |
| 109. C2×C8 | C4×D17 | semidirect |
| 133. C8 | C2×C4×D17 | semidirect |
| 146. C2 | #97×D17 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D17 | 2 |
| C2×C42×D17 | 2 |
| C2×#10587474 | 2 |
| C2×#10587486 | 2 |
| #97×D17 | 2 |
| C2×C17×#97 | 2 |
| C22×#97 | 17 |