Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
536 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #11762849 | C2 | direct (N × H) |
| 4. C2×#10587478 | C2 | semidirect |
| 5. C2×#10587479 | C2 | semidirect |
| 19. C2×#63223 | C4 | semidirect |
| 22. #10587479 | C22 | semidirect |
| 23. #10587478 | C22 | semidirect |
| 45. #63223 | C2×C4 | semidirect |
| 46. C2×#3622 | C2×C4 | semidirect |
| 69. #3622 | C22×C4 | semidirect |
| 93. C2×C17 | #428 | semidirect |
| 114. C17 | C2×#428 | semidirect |
| 177. C2 | #11762849 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63223 | 2 |
| C2×#10587612 | 2 |
| #11762849 | 2 |
| C2×#10587478 | 2 |
| C2×#10587479 | 2 |
| C22×C4⋊C4×C17 | 2 |
| C2×#428 | 17 |