Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
572 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 288 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. #11763774 | C2 | semidirect |
| 3. C4×#63243 | C2 | semidirect |
| 4. C4×#63242 | C2 | semidirect |
| 7. #10587680 | C4 | direct (N × H) |
| 28. #63243 | C2×C4 | semidirect |
| 29. #63242 | C2×C4 | semidirect |
| 58. C4×C17 | #131 | semidirect |
| 60. Dic17 | #131 | semidirect |
| 85. C17 | C4×#131 | semidirect |
| 126. C4 | #10587680 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587680 | 2 |
| #11763774 | 2 |
| C4×#63243 | 2 |
| C4×#63242 | 2 |
| C4×#63256 | 2 |
| C4×#131 | 17 |