Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#22583543 | C2 | semidirect |
| 3. C2×#22583534 | C2 | semidirect |
| 5. C2×#22583521 | C2 | semidirect |
| 7. #391×C283 | C2 | semidirect |
| 11. C2×#17985379 | C4 | semidirect |
| 68. C283⋊C8 | C22⋊C4 | semidirect |
| 112. C283 | #1973 | semidirect |
| 119. #391 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17985379 | 2 |
| C2×#22583543 | 2 |
| C2×#22583534 | 2 |
| C2×#22583530 | 2 |
| C2×#22583521 | 2 |
| #31826367 | 2 |
| #391×C283 | 2 |
| #1973 | 283 |