Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31826803 | C2 | semidirect |
| 3. #31826798 | C2 | semidirect |
| 4. #31826793 | C2 | semidirect |
| 5. #31826505 | C2 | semidirect |
| 6. #31826474 | C2 | semidirect |
| 18. #22583543 | C22 | semidirect |
| 19. #22583541 | C22 | semidirect |
| 20. #22583534 | C22 | semidirect |
| 21. #22583534 | C22 | semidirect |
| 116. C283 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583569 | 2 |
| #31826803 | 2 |
| #31826798 | 2 |
| #31826793 | 2 |
| #31826505 | 2 |
| #31826474 | 2 |
| #31826429 | 2 |
| C2×C22⋊Q8×C283 | 2 |
| #3095 | 283 |