Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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. #31826948 | C2 | semidirect |
| 3. #31826471 | C2 | semidirect |
| 4. #31826367 | C2 | semidirect |
| 5. #31826233 | C2 | semidirect |
| 6. #31826225 | C2 | semidirect |
| 7. C2×#104×C283 | C2 | semidirect |
| 10. #22583635 | C4 | semidirect |
| 34. C2×D1132 | C2×C4 | semidirect |
| 40. #17985376 | C2×C4 | semidirect |
| 85. Q8×C283 | C22⋊C4 | semidirect |
| 89. D4×C283 | C22⋊C4 | semidirect |
| 132. C283 | #1883 | semidirect |
| 136. C2×#104 | D283 | semidirect |
| 208. Q8 | (C2×D283)⋊C4 | semidirect |
| 216. D4 | (C2×D283)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583635 | 2 |
| #31826948 | 2 |
| #31826471 | 2 |
| #31826367 | 2 |
| #31826233 | 2 |
| #31826225 | 2 |
| C2×#104×C283 | 2 |
| #1883 | 283 |