Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#22583575 | C2 | semidirect |
| 3. #31826783 | C2 | semidirect |
| 4. #31826749 | C2 | semidirect |
| 5. #31826664 | C2 | semidirect |
| 6. #31826606 | C2 | semidirect |
| 7. #31826603 | C2 | semidirect |
| 8. #31826556 | C2 | semidirect |
| 9. #31826552 | C2 | semidirect |
| 10. #31826515 | C2 | semidirect |
| 11. #481×C283 | C2 | semidirect |
| 86. Dic566 | #41 | semidirect |
| 96. C2×Dic283 | SD16 | semidirect |
| 140. C283 | #3103 | semidirect |
| 145. #481 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827010 | 2 |
| C2×#22583575 | 2 |
| #31826783 | 2 |
| #31826749 | 2 |
| #31826664 | 2 |
| #31826606 | 2 |
| #31826603 | 2 |
| #31826556 | 2 |
| #31826552 | 2 |
| #31826515 | 2 |
| #481×C283 | 2 |
| #3103 | 283 |