Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22583641 | C2 | semidirect |
| 3. #31826844 | C2 | semidirect |
| 4. #31826721 | C2 | semidirect |
| 5. #31826675 | C2 | semidirect |
| 6. #31826667 | C2 | semidirect |
| 7. #31826625 | C2 | semidirect |
| 8. #31826621 | C2 | semidirect |
| 9. C4×#17985379 | C2 | semidirect |
| 10. #31826543 | C2 | semidirect |
| 11. D4×Q8×C283 | C2 | semidirect |
| 53. #17985379 | D4 | semidirect |
| 124. C4×C283 | #137 | semidirect |
| 134. C283 | #3276 | semidirect |
| 137. D4×Q8 | D283 | semidirect |
| 261. C4 | #22583641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583641 | 2 |
| #31827120 | 2 |
| #31826844 | 2 |
| #31826721 | 2 |
| #31826675 | 2 |
| #31826667 | 2 |
| #31826625 | 2 |
| #31826621 | 2 |
| C4×#17985379 | 2 |
| #31826543 | 2 |
| D4×Q8×C283 | 2 |
| #3276 | 283 |