Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
368 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 2. #31826870 | C2 | semidirect |
| 3. #31826845 | C2 | semidirect |
| 4. #31826816 | C2 | semidirect |
| 6. C4×Dic1132 | C2 | semidirect |
| 52. C2×C4×C283 | Q16 | semidirect |
| 77. C283 | #3170 | semidirect |
| 130. C2×C4 | Dic1132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827022 | 2 |
| #31826870 | 2 |
| #31826845 | 2 |
| #31826816 | 2 |
| #31826706 | 2 |
| C4×Dic1132 | 2 |
| C2×C4×C8×C283 | 2 |
| #3170 | 283 |