Finite Group DatabasebetaFinite Group DatabasebetaOrder 832.
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. C22×Dic26 | C2 | semidirect |
| 3. C2×C13×C4⋊C4 | C2 | semidirect |
| 6. C2×#6101 | C2 | semidirect |
| 7. C2×#6101 | C2 | semidirect |
| 8. #88150 | C2 | direct (N × H) |
| 19. C2×Dic26 | C22 | semidirect |
| 20. C13×C4⋊C4 | C22 | semidirect |
| 23. #6101 | C22 | semidirect |
| 24. #6101 | C22 | semidirect |
| 28. C22×D13 | Q8 | semidirect |
| 52. C2×D13 | C2×Q8 | semidirect |
| 64. C2×C4⋊C4 | D13 | semidirect |
| 67. C2×C13 | C22⋊Q8 | semidirect |
| 85. C4⋊C4 | C2×D13 | semidirect |
| 88. C13 | C2×C22⋊Q8 | semidirect |
| 123. C2 | #88150 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D13 | 2 |
| C22×Dic26 | 2 |
| C2×C13×C4⋊C4 | 2 |
| C2×#6103 | 2 |
| C2×#6101 | 2 |
| #88150 | 2 |
| C2×C22⋊Q8 | 13 |