Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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×#22583635 | C2 | semidirect |
| 2. C2×C4×D1132 | C2 | semidirect |
| 3. #31826677 | C2 | semidirect |
| 4. #31826667 | C2 | semidirect |
| 5. #31826657 | C2 | semidirect |
| 6. #31826489 | C2 | semidirect |
| 7. #31826466 | C2 | semidirect |
| 8. #532×C283 | C2 | semidirect |
| 21. C4⋊(C283⋊C8) | C22 | semidirect |
| 22. C4⋊(C283⋊C8) | C22 | semidirect |
| 23. #22583534 | C22 | semidirect |
| 24. #22583531 | C22 | semidirect |
| 26. C4⋊Q8×C283 | C22 | semidirect |
| 27. #127×C283 | C22 | semidirect |
| 28. #124×C283 | C22 | semidirect |
| 37. C2×D1132 | D4 | semidirect |
| 119. C4×C283 | AGL(1,ℤ/8) | semidirect |
| 129. C283 | #3036 | semidirect |
| 132. #532 | D283 | semidirect |
| 146. C4⋊Q8 | C2×D283 | semidirect |
| 147. #127 | C2×D283 | semidirect |
| 148. #124 | C2×D283 | semidirect |
| 250. C4 | #22583635 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583635 | 2 |
| C2×C4×D1132 | 2 |
| #31826677 | 2 |
| #31826667 | 2 |
| #31826657 | 2 |
| #31826489 | 2 |
| #31826466 | 2 |
| #532×C283 | 2 |
| #3036 | 283 |