Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1252 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 261 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. C22×#63227 | C2 | semidirect |
| 3. C22×#63227 | C2 | semidirect |
| 4. #11762726 | C2 | direct (N × H) |
| 5. C2×#10587502 | C2 | semidirect |
| 6. C22×C4⋊C4×C17 | C2 | semidirect |
| 16. C2×C4⋊C4×C17 | C22 | semidirect |
| 19. C2×#63227 | C22 | semidirect |
| 20. C2×#63227 | C22 | semidirect |
| 21. #10587502 | C22 | semidirect |
| 37. C22×C4×C17 | D4 | semidirect |
| 80. C2×C4×C17 | C2×D4 | semidirect |
| 110. C22×C4⋊C4 | D17 | semidirect |
| 115. C2×C17 | #394 | semidirect |
| 131. C2×C4⋊C4 | C2×D17 | semidirect |
| 137. C17 | C2×#394 | semidirect |
| 159. C22×C4 | D68 | semidirect |
| 200. C2×C4 | C2×D68 | semidirect |
| 225. C2 | #11762726 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D68 | 2 |
| C22×#63227 | 2 |
| #11762726 | 2 |
| C2×#10587502 | 2 |
| C22×C4⋊C4×C17 | 2 |
| C2×#394 | 17 |