Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#17985380 | C2 | semidirect |
| 2. C22×#17985377 | C2 | semidirect |
| 3. C2×#22583598 | C2 | semidirect |
| 4. #31826852 | C2 | direct (N × H) |
| 5. C2×#22583521 | C2 | semidirect |
| 6. C2×#127×C283 | C2 | semidirect |
| 10. C2×#17985380 | C22 | semidirect |
| 12. C2×#17985377 | C22 | semidirect |
| 15. #22583598 | C22 | semidirect |
| 17. #22583521 | C22 | semidirect |
| 21. #127×C283 | C22 | semidirect |
| 33. C2×C283⋊C8 | D4 | semidirect |
| 56. C283⋊C8 | C2×D4 | semidirect |
| 84. C2×C283 | #496 | semidirect |
| 88. C283 | C2×#496 | semidirect |
| 92. C2×#127 | D283 | semidirect |
| 106. #127 | C2×D283 | semidirect |
| 174. C2 | #31826852 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985380 | 2 |
| C22×#17985377 | 2 |
| C2×#22583598 | 2 |
| #31826852 | 2 |
| C2×#22583521 | 2 |
| C2×#127×C283 | 2 |
| C2×#496 | 283 |