Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 3. #31826775 | C2 | semidirect |
| 4. #31826771 | C2 | semidirect |
| 5. #31826759 | C2 | semidirect |
| 6. #31826749 | C2 | semidirect |
| 47. C2×Dic566 | Q8 | semidirect |
| 129. C283 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827018 | 2 |
| C2×#22583575 | 2 |
| #31826775 | 2 |
| #31826771 | 2 |
| #31826759 | 2 |
| #31826749 | 2 |
| #31826505 | 2 |
| #31826488 | 2 |
| #31826475 | 2 |
| #31826473 | 2 |
| #428×C283 | 2 |
| #3078 | 283 |