Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22583643 | C2 | semidirect |
| 3. C2×C4×Dic566 | C2 | semidirect |
| 4. #31826688 | C2 | semidirect |
| 5. #31826676 | C2 | semidirect |
| 6. #31826666 | C2 | semidirect |
| 7. #31826467 | C2 | semidirect |
| 8. #423×C283 | C2 | semidirect |
| 38. C2×Dic566 | D4 | semidirect |
| 109. C4×C283 | #137 | semidirect |
| 120. C283 | #3037 | semidirect |
| 128. #423 | D283 | semidirect |
| 233. C4 | #22583643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583643 | 2 |
| #31827015 | 2 |
| C2×C4×Dic566 | 2 |
| #31826688 | 2 |
| #31826676 | 2 |
| #31826666 | 2 |
| #31826467 | 2 |
| #423×C283 | 2 |
| #3037 | 283 |