Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C2×#10587628 | C2 | semidirect |
| 3. #11763201 | C2 | semidirect |
| 4. #11763188 | C2 | semidirect |
| 5. #11763183 | C2 | semidirect |
| 6. C4×#63223 | C2 | semidirect |
| 7. C2×C17×C4⋊Q8 | C2 | semidirect |
| 47. #63223 | D4 | semidirect |
| 77. C4×C17 | #137 | semidirect |
| 82. C2×C4⋊Q8 | D17 | semidirect |
| 109. C17 | #3152 | semidirect |
| 161. C4 | #10587628 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| #11763359 | 2 |
| #11763201 | 2 |
| #11763188 | 2 |
| #11763183 | 2 |
| C4×#63223 | 2 |
| C2×C17×C4⋊Q8 | 2 |
| #3152 | 17 |