Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #31826945 | C2 | semidirect |
| 3. #31826578 | C2 | semidirect |
| 4. #31826573 | C2 | semidirect |
| 5. C4×#17985381 | C2 | semidirect |
| 6. C2×#22583542 | C2 | semidirect |
| 7. #31826467 | C2 | semidirect |
| 8. #405×C283 | C2 | semidirect |
| 10. #22583632 | C4 | semidirect |
| 30. #17985392 | C2×C4 | semidirect |
| 37. Dic1132 | C2×C4 | semidirect |
| 38. #17985381 | C2×C4 | semidirect |
| 39. D2264 | C2×C4 | semidirect |
| 47. C2×C8×C283 | C2×C4 | semidirect |
| 90. C283 | #2952 | semidirect |
| 99. #405 | D283 | semidirect |
| 133. C2×C8 | C4×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583632 | 2 |
| #31826945 | 2 |
| #31826578 | 2 |
| #31826573 | 2 |
| C4×#17985381 | 2 |
| C2×#22583542 | 2 |
| #31826467 | 2 |
| #405×C283 | 2 |
| #2952 | 283 |