Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31827022 | C2 | semidirect |
| 3. #31826830 | C2 | semidirect |
| 4. #31826812 | C2 | semidirect |
| 5. #31826471 | C2 | semidirect |
| 6. C4×M16×C283 | C2 | semidirect |
| 9. #22583610 | C22 | semidirect |
| 13. #22583602 | C22 | semidirect |
| 17. #22583532 | C22 | semidirect |
| 20. #97×C283 | C22 | semidirect |
| 21. C4×C8×C283 | C22 | semidirect |
| 74. C283 | #3138 | semidirect |
| 81. C4×M16 | D283 | semidirect |
| 95. #97 | C2×D283 | semidirect |
| 96. C4×C8 | C2×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827022 | 2 |
| C2×#22583607 | 2 |
| #31826830 | 2 |
| #31826812 | 2 |
| #31826471 | 2 |
| C4×M16×C283 | 2 |
| #3138 | 283 |