Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
176 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 73 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. C8×Dic34 | C2 | semidirect |
| 3. #11762561 | C2 | semidirect |
| 4. #11762539 | C2 | semidirect |
| 6. #11762531 | C2 | semidirect |
| 33. #63229 | C8 | semidirect |
| 53. Dic34 | C2×C8 | semidirect |
| 60. #3622 | C2×C8 | semidirect |
| 100. C17 | SD16⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic34 | 2 |
| C4×#63229 | 2 |
| #11762561 | 2 |
| #11762539 | 2 |
| D4⋊#3622 | 2 |
| #11762531 | 2 |
| C8×D4×C17 | 2 |
| SD16⋊C8 | 17 |