Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
160 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 47 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×#22583554 | C2 | semidirect |
| 2. C2×#22583549 | C2 | semidirect |
| 3. #31826707 | C2 | semidirect |
| 5. #31826290 | C2 | semidirect |
| 6. #31826270 | C2 | semidirect |
| 7. #357×C283 | C2 | semidirect |
| 33. C283⋊C16 | D4 | semidirect |
| 75. C283 | #2220 | semidirect |
| 83. #357 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583554 | 2 |
| C2×#22583549 | 2 |
| #31826707 | 2 |
| #31826698 | 2 |
| #31826290 | 2 |
| #31826270 | 2 |
| #357×C283 | 2 |
| #2220 | 283 |