Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
420 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11763415 | C2 | semidirect |
| 2. #11763377 | C2 | semidirect |
| 3. #11763199 | C2 | semidirect |
| 4. #11763186 | C2 | semidirect |
| 5. #11763175 | C2 | semidirect |
| 6. #11763027 | C2 | semidirect |
| 7. #11763003 | C2 | semidirect |
| 8. #11762957 | C2 | semidirect |
| 9. #11762944 | C2 | semidirect |
| 10. #11762868 | C2 | semidirect |
| 11. C17×#488 | C2 | semidirect |
| 14. C17×#125 | C22 | semidirect |
| 17. C2×#63230 | C22 | semidirect |
| 21. C2×D136 | C22 | semidirect |
| 25. #10587579 | C22 | semidirect |
| 29. #10587560 | C22 | semidirect |
| 31. C17×#103 | C22 | semidirect |
| 33. C4×C8×C17 | C22 | semidirect |
| 35. #10587485 | C22 | semidirect |
| 37. #10587480 | C22 | semidirect |
| 38. #10587474 | C22 | semidirect |
| 127. #488 | D17 | semidirect |
| 149. #125 | C2×D17 | semidirect |
| 160. #103 | C2×D17 | semidirect |
| 166. C4×C8 | C2×D17 | semidirect |
| 167. C17 | #3220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763415 | 2 |
| #11763377 | 2 |
| #11763199 | 2 |
| #11763186 | 2 |
| #11763175 | 2 |
| #11763027 | 2 |
| #11763003 | 2 |
| #11762957 | 2 |
| #11762944 | 2 |
| #11762868 | 2 |
| C17×#488 | 2 |
| #3220 | 17 |