Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. C4×Q8×C29 | C2 | semidirect |
| 3. #11745306 | C2 | semidirect |
| 6. #11745251 | C2 | semidirect |
| 7. #11745250 | C2 | semidirect |
| 10. C4×Dic58 | C2 | semidirect |
| 11. C4×Dic58 | C2 | semidirect |
| 49. C4×D29 | Q8 | semidirect |
| 79. C4×Q8 | D29 | semidirect |
| 82. C29 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C29 | 2 |
| #11745308 | 2 |
| #11745306 | 2 |
| #11745259 | 2 |
| #11745258 | 2 |
| #11745251 | 2 |
| #11745250 | 2 |
| #11745234 | 2 |
| C42×D29 | 2 |
| C4×Dic58 | 2 |
| #533 | 29 |