Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22583632 | C2 | semidirect |
| 2. #31827043 | C2 | semidirect |
| 3. #31826723 | C2 | semidirect |
| 4. #31826718 | C2 | semidirect |
| 5. #31826694 | C2 | semidirect |
| 6. C2×#22583542 | C2 | semidirect |
| 7. #31826467 | C2 | semidirect |
| 8. C2×#131×C283 | C2 | semidirect |
| 56. C2×C8×C283 | D4 | semidirect |
| 105. C283 | #3060 | semidirect |
| 108. C2×#131 | D283 | semidirect |
| 157. C2×C8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| #31827043 | 2 |
| #31826723 | 2 |
| #31826718 | 2 |
| #31826694 | 2 |
| C2×#22583542 | 2 |
| #31826467 | 2 |
| C2×#131×C283 | 2 |
| #3060 | 283 |