Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C4⋊C4×D17 | C2 | semidirect |
| 3. #11763129 | C2 | direct (N × H) |
| 4. C2×#10587479 | C2 | semidirect |
| 5. C2×#10587492 | C2 | semidirect |
| 6. C2×#10587480 | C2 | semidirect |
| 7. C2×#10587491 | C2 | semidirect |
| 8. C2×C17×#106 | C2 | semidirect |
| 23. C4⋊C4×D17 | C22 | semidirect |
| 24. C17×#106 | C22 | semidirect |
| 25. #10587492 | C22 | semidirect |
| 26. #10587491 | C22 | semidirect |
| 27. #10587480 | C22 | semidirect |
| 28. #10587479 | C22 | semidirect |
| 115. C2×#106 | D17 | semidirect |
| 119. C2×C17 | #481 | semidirect |
| 141. #106 | C2×D17 | semidirect |
| 145. C17 | C2×#481 | semidirect |
| 229. C2 | #11763129 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587581 | 2 |
| C2×C4⋊C4×D17 | 2 |
| #11763129 | 2 |
| C2×#10587479 | 2 |
| C2×#10587492 | 2 |
| C2×#10587480 | 2 |
| C2×#10587491 | 2 |
| C2×C17×#106 | 2 |
| C2×#481 | 17 |