Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
792 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 218 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. C23×#3624 | C2 | semidirect |
| 3. #11763782 | C2 | direct (N × H) |
| 4. C2×#10587543 | C2 | semidirect |
| 5. C2×C22⋊#3624 | C2 | semidirect |
| 19. C2×#63247 | C22 | semidirect |
| 23. C22×#3624 | C22 | semidirect |
| 24. C22⋊#3624 | C22 | semidirect |
| 25. #10587543 | C22 | semidirect |
| 124. C2×C17 | #408 | semidirect |
| 147. C17 | C2×#408 | semidirect |
| 240. C2 | #11763782 | 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 |
| C23×#3624 | 2 |
| #11763782 | 2 |
| C2×#10587543 | 2 |
| C2×C22⋊#3624 | 2 |
| C22×#63254 | 2 |
| C2×#408 | 17 |