Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
348 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×C4⋊#3622 | C2 | semidirect |
| 4. #11762564 | C2 | semidirect |
| 28. C22⋊C4×C17 | C8 | semidirect |
| 55. C2×C4×C17 | C2×C8 | semidirect |
| 68. C22×C17 | C4⋊C8 | semidirect |
| 103. C17 | #1850 | semidirect |
| 122. C22⋊C4 | #3622 | semidirect |
| 140. C2×C4 | C2×#3622 | semidirect |
| 153. C22 | C4⋊#3622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3622 | 2 |
| C2×C4⋊#3622 | 2 |
| C2×C22⋊#3622 | 2 |
| #11762564 | 2 |
| C4×C22⋊C4×C17 | 2 |
| #1850 | 17 |