Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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×#22583610 | C2 | semidirect |
| 2. #31826811 | C2 | direct (N × H) |
| 3. C2×#22583531 | C2 | semidirect |
| 4. C2×C4×C283⋊C8 | C2 | semidirect |
| 9. #22583610 | C22 | semidirect |
| 12. #22583531 | C22 | semidirect |
| 13. C4×C283⋊C8 | C22 | semidirect |
| 75. C2×C283 | #486 | semidirect |
| 79. C283 | C2×#486 | semidirect |
| 155. C2 | #31826811 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583610 | 2 |
| #31826811 | 2 |
| C2×#22583531 | 2 |
| C2×C4×C283⋊C8 | 2 |
| C2×#127×C283 | 2 |
| C2×#486 | 283 |