Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
| 2. #11745309 | C2 | semidirect |
| 3. #11745308 | C2 | semidirect |
| 4. #11745260 | C2 | semidirect |
| 6. #11745256 | C2 | semidirect |
| 7. #11745252 | C2 | semidirect |
| 8. C4×D116 | C2 | semidirect |
| 9. C4×D116 | C2 | semidirect |
| 10. #11745234 | C2 | semidirect |
| 11. C42×D29 | C2 | semidirect |
| 81. C4×Q8 | D29 | semidirect |
| 86. C29 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×C29 | 2 |
| #11745309 | 2 |
| #11745308 | 2 |
| #11745260 | 2 |
| #11745257 | 2 |
| #11745256 | 2 |
| #11745252 | 2 |
| C4×D116 | 2 |
| #11745234 | 2 |
| C42×D29 | 2 |
| #529 | 29 |