Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
756 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 202 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. C22×#63247 | C2 | semidirect |
| 2. #11763796 | C2 | direct (N × H) |
| 3. C2×#10587545 | C2 | semidirect |
| 4. C2×#10587553 | C2 | semidirect |
| 21. C2×#63247 | C22 | semidirect |
| 23. #10587553 | C22 | semidirect |
| 24. #10587545 | C22 | semidirect |
| 142. C2×C17 | #413 | semidirect |
| 164. C17 | C2×#413 | semidirect |
| 277. C2 | #11763796 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63247 | 2 |
| #11763796 | 2 |
| C2×#10587545 | 2 |
| C2×#10587553 | 2 |
| C22×#63254 | 2 |
| C2×#413 | 17 |