Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#10587560 | C2 | semidirect |
| 2. #11763199 | C2 | semidirect |
| 3. #11763175 | C2 | semidirect |
| 4. #11763009 | C2 | semidirect |
| 5. #11763004 | C2 | semidirect |
| 6. #11762959 | C2 | semidirect |
| 7. #11762942 | C2 | semidirect |
| 8. #11762866 | C2 | semidirect |
| 9. C17×#529 | C2 | semidirect |
| 14. C17×#125 | C22 | semidirect |
| 15. C17×#124 | C22 | semidirect |
| 19. C4×Q8×C17 | C22 | semidirect |
| 21. C4×D4×C17 | C22 | semidirect |
| 24. C2×#63230 | C22 | semidirect |
| 25. C2×#63228 | C22 | semidirect |
| 31. #10587480 | C22 | semidirect |
| 32. #10587480 | C22 | semidirect |
| 33. C4⋊#3622 | C22 | semidirect |
| 34. #10587474 | C22 | semidirect |
| 123. #529 | D17 | semidirect |
| 147. #125 | C2×D17 | semidirect |
| 148. #124 | C2×D17 | semidirect |
| 152. C4×Q8 | C2×D17 | semidirect |
| 154. C4×D4 | C2×D17 | semidirect |
| 162. C17 | #3217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587560 | 2 |
| #11763199 | 2 |
| #11763175 | 2 |
| #11763009 | 2 |
| #11763004 | 2 |
| #11762959 | 2 |
| #11762942 | 2 |
| #11762866 | 2 |
| C17×#529 | 2 |
| #3217 | 17 |