Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
364 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 197 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. #31826595 | C2 | semidirect |
| 3. C8×Dic566 | C2 | semidirect |
| 34. C2×C8×C283 | Q8 | semidirect |
| 67. C283 | #2960 | semidirect |
| 97. C2×C8 | Dic566 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827022 | 2 |
| #31826595 | 2 |
| C8×Dic566 | 2 |
| #31826491 | 2 |
| #31826489 | 2 |
| #31826420 | 2 |
| C2×C4×C8×C283 | 2 |
| #2960 | 283 |