Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. #11763383 | C2 | semidirect |
| 4. #11763202 | C2 | semidirect |
| 5. #11763194 | C2 | semidirect |
| 6. #11763187 | C2 | semidirect |
| 7. #11762764 | C2 | semidirect |
| 8. C22×Q16×C17 | C2 | semidirect |
| 95. C22×Q16 | D17 | semidirect |
| 126. C17 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587628 | 2 |
| C2×#10587590 | 2 |
| #11763383 | 2 |
| #11763202 | 2 |
| #11763194 | 2 |
| #11763187 | 2 |
| #11762764 | 2 |
| C22×Q16×C17 | 2 |
| #3156 | 17 |