Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 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×#22583636 | C2 | semidirect |
| 2. C4×#17985392 | C2 | semidirect |
| 3. #31826662 | C2 | semidirect |
| 4. #31826657 | C2 | semidirect |
| 5. #31826489 | C2 | semidirect |
| 6. #31826470 | C2 | semidirect |
| 7. C2×#127×C283 | C2 | semidirect |
| 10. C2×#17985380 | C22 | semidirect |
| 11. C2×#17985377 | C22 | semidirect |
| 13. C4×Dic566 | C22 | semidirect |
| 14. C4×D1132 | C22 | semidirect |
| 19. C4⋊(C283⋊C8) | C22 | semidirect |
| 20. #22583531 | C22 | semidirect |
| 28. #17985392 | D4 | semidirect |
| 59. Dic566 | C2×D4 | semidirect |
| 61. D1132 | C2×D4 | semidirect |
| 94. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 104. C283 | #3038 | semidirect |
| 107. C2×#127 | D283 | semidirect |
| 201. C4 | #22583636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583636 | 2 |
| C4×#17985392 | 2 |
| #31826662 | 2 |
| #31826657 | 2 |
| #31826489 | 2 |
| #31826470 | 2 |
| C2×#127×C283 | 2 |
| #3038 | 283 |