Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
620 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×D8×D17 | C2 | semidirect |
| 2. #11763444 | C2 | semidirect |
| 3. #11763042 | C2 | semidirect |
| 4. #11763001 | C2 | semidirect |
| 5. #11762941 | C2 | semidirect |
| 6. C4×D136 | C2 | semidirect |
| 7. C8×D68 | C2 | semidirect |
| 8. C17×#493 | C2 | semidirect |
| 10. C2×D4×D17 | C22 | semidirect |
| 11. C2×D8×C17 | C22 | semidirect |
| 12. C2×D8×C17 | C22 | semidirect |
| 13. C17×#127 | C22 | semidirect |
| 15. #10587624 | C22 | semidirect |
| 17. C2×#63228 | C22 | semidirect |
| 20. C2×C8×D17 | C22 | semidirect |
| 22. C4×D68 | C22 | semidirect |
| 23. C4×C8×C17 | C22 | semidirect |
| 24. #10587503 | C22 | semidirect |
| 25. #10587492 | C22 | semidirect |
| 26. #10587491 | C22 | semidirect |
| 27. #10587489 | C22 | semidirect |
| 28. C4⋊#3622 | C22 | semidirect |
| 54. D136 | D4 | semidirect |
| 74. D68 | D8 | semidirect |
| 75. D68 | C2×D4 | semidirect |
| 80. C8×C17 | C2×D4 | semidirect |
| 93. C2×D17 | C2×D8 | semidirect |
| 95. C4×C17 | C2×D8 | semidirect |
| 102. #493 | D17 | semidirect |
| 119. C2×D8 | C2×D17 | semidirect |
| 120. C2×D8 | C2×D17 | semidirect |
| 122. #127 | C2×D17 | semidirect |
| 133. C4×C8 | C2×D17 | semidirect |
| 134. C17 | D4×D8 | semidirect |
| 187. C8 | D4×D17 | semidirect |
| 202. C4 | D8×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D17 | 2 |
| #11763444 | 2 |
| #11763042 | 2 |
| #11763001 | 2 |
| #11762941 | 2 |
| C4×D136 | 2 |
| C8×D68 | 2 |
| C17×#493 | 2 |
| D4×D8 | 17 |