Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 139 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. Q8×Dic566 | C2 | semidirect |
| 3. #31826812 | C2 | semidirect |
| 4. #31826756 | C2 | semidirect |
| 5. #31826666 | C2 | semidirect |
| 6. C4×#17985381 | C2 | semidirect |
| 7. C8×Q8×C283 | C2 | semidirect |
| 46. Dic566 | #41 | semidirect |
| 55. Q8×C283 | SD16 | semidirect |
| 76. C283 | #3362 | semidirect |
| 83. C8×Q8 | D283 | semidirect |
| 124. Q8 | #17985381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic566 | 2 |
| #31827137 | 2 |
| #31826812 | 2 |
| #31826756 | 2 |
| #31826666 | 2 |
| C4×#17985381 | 2 |
| C8×Q8×C283 | 2 |
| #3362 | 283 |