Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
132 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 51 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×D4×C29 | C2 | semidirect |
| 3. C4×D116 | C2 | semidirect |
| 4. #11745180 | C2 | semidirect |
| 5. #11745157 | C2 | semidirect |
| 6. #11745156 | C2 | semidirect |
| 7. #11745151 | C2 | semidirect |
| 15. #90782 | C4 | semidirect |
| 23. D4×C29 | C2×C4 | semidirect |
| 31. D116 | C2×C4 | semidirect |
| 34. #6597 | C2×C4 | semidirect |
| 56. C4×D4 | D29 | semidirect |
| 61. C29 | #442 | semidirect |
| 79. D4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×C29 | 2 |
| C2×#90782 | 2 |
| C4×D116 | 2 |
| #11745180 | 2 |
| #11745157 | 2 |
| #11745156 | 2 |
| #11745151 | 2 |
| #442 | 29 |