Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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×#10587498 | C2 | semidirect |
| 2. C4×Dic68 | C2 | semidirect |
| 3. C4⋊#63214 | C2 | semidirect |
| 4. #11762610 | C2 | semidirect |
| 30. Dic68 | D4 | semidirect |
| 53. C4×C17 | SD32 | semidirect |
| 77. C17 | #2207 | semidirect |
| 116. C4 | #10587498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587498 | 2 |
| C4×Dic68 | 2 |
| C4⋊#63214 | 2 |
| #11762610 | 2 |
| C17×#493 | 2 |
| #2207 | 17 |