Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#22583635 | C2 | semidirect |
| 2. C22×#17985379 | C2 | semidirect |
| 3. #31827029 | C2 | semidirect |
| 4. #31826610 | C2 | semidirect |
| 5. #31826604 | C2 | semidirect |
| 6. #31826474 | C2 | semidirect |
| 7. #31826461 | C2 | semidirect |
| 8. #31826432 | C2 | semidirect |
| 9. C2×2−1+4×C283 | C2 | semidirect |
| 23. #22583534 | C22 | semidirect |
| 24. #22583534 | C22 | semidirect |
| 25. #22583531 | C22 | semidirect |
| 26. C22⋊(C283⋊C8) | C22 | semidirect |
| 33. C2×#41×C283 | C22 | semidirect |
| 36. C22×Q8×C283 | C22 | semidirect |
| 61. #41×C283 | D4 | semidirect |
| 69. C2×Q8×C283 | D4 | semidirect |
| 145. C283 | #3010 | semidirect |
| 147. C2×2−1+4 | D283 | semidirect |
| 162. C2×#41 | C2×D283 | semidirect |
| 165. C22×Q8 | C2×D283 | semidirect |
| 191. #41 | C22⋊D283 | semidirect |
| 199. C2×Q8 | C22⋊D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583635 | 2 |
| C22×#17985379 | 2 |
| #31827029 | 2 |
| #31826610 | 2 |
| #31826604 | 2 |
| #31826474 | 2 |
| #31826461 | 2 |
| #31826432 | 2 |
| C2×2−1+4×C283 | 2 |
| #3010 | 283 |