Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 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. #31827022 | C2 | semidirect |
| 3. #31826863 | C2 | semidirect |
| 4. #31826838 | C2 | semidirect |
| 5. #31826816 | C2 | semidirect |
| 6. #31826812 | C2 | semidirect |
| 7. #31826694 | C2 | semidirect |
| 8. C4×#17985381 | C2 | semidirect |
| 9. C2×C4×C8×C283 | C2 | semidirect |
| 82. C2×C4×C283 | SD16 | semidirect |
| 90. C8×C283 | #41 | semidirect |
| 112. C283 | #3167 | semidirect |
| 122. C2×C4×C8 | D283 | semidirect |
| 195. C2×C4 | #17985381 | semidirect |
| 203. C8 | #17985392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827022 | 2 |
| #31827015 | 2 |
| #31826863 | 2 |
| #31826838 | 2 |
| #31826816 | 2 |
| #31826812 | 2 |
| #31826694 | 2 |
| C4×#17985381 | 2 |
| C2×C4×C8×C283 | 2 |
| #3167 | 283 |