Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #11762848 | C2 | direct (N × H) |
| 5. C2×#10587489 | C2 | semidirect |
| 6. C2×#10587478 | C2 | semidirect |
| 7. C2×#10587479 | C2 | semidirect |
| 8. C2×C17×#106 | C2 | semidirect |
| 20. C2×#63218 | C4 | semidirect |
| 26. C17×#106 | C22 | semidirect |
| 27. #10587489 | C22 | semidirect |
| 28. #10587479 | C22 | semidirect |
| 29. #10587478 | C22 | semidirect |
| 43. C2×C8×C17 | C2×C4 | semidirect |
| 56. C2×#3622 | C2×C4 | semidirect |
| 58. #63218 | C2×C4 | semidirect |
| 82. C8×C17 | C22×C4 | semidirect |
| 83. #3622 | C22×C4 | semidirect |
| 108. C2×#106 | D17 | semidirect |
| 109. C2×C17 | #428 | semidirect |
| 134. #106 | C2×D17 | semidirect |
| 135. C17 | C2×#428 | semidirect |
| 152. C2×C8 | C4×D17 | semidirect |
| 189. C8 | C2×C4×D17 | semidirect |
| 207. C2 | #11762848 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63218 | 2 |
| C2×#10587578 | 2 |
| C2×C4⋊C4×D17 | 2 |
| #11762848 | 2 |
| C2×#10587489 | 2 |
| C2×#10587478 | 2 |
| C2×#10587479 | 2 |
| C2×C17×#106 | 2 |
| C2×#428 | 17 |