Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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×#22583556 | C2 | semidirect |
| 2. C2×#22583554 | C2 | semidirect |
| 3. #31826706 | C2 | semidirect |
| 4. #31826269 | C2 | semidirect |
| 5. #31826266 | C2 | semidirect |
| 6. C22⋊(C283⋊C16) | C2 | semidirect |
| 85. C283 | #2189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583556 | 2 |
| C2×#22583554 | 2 |
| #31826706 | 2 |
| #31826269 | 2 |
| #31826266 | 2 |
| C22⋊(C283⋊C16) | 2 |
| C2×#135×C283 | 2 |
| #2189 | 283 |