Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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×#22583643 | C2 | semidirect |
| 2. C2×#22583640 | C2 | semidirect |
| 4. C2×#22583575 | C2 | semidirect |
| 5. #31826690 | C2 | semidirect |
| 6. #31826686 | C2 | semidirect |
| 7. #31826674 | C2 | semidirect |
| 8. #31826664 | C2 | semidirect |
| 9. #31826488 | C2 | semidirect |
| 10. #31826464 | C2 | semidirect |
| 11. #417×C283 | C2 | semidirect |
| 49. C2×Dic566 | D4 | semidirect |
| 150. Dic283 | #137 | semidirect |
| 157. C283 | #3037 | semidirect |
| 169. #417 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583643 | 2 |
| C2×#22583640 | 2 |
| #31827011 | 2 |
| C2×#22583575 | 2 |
| #31826690 | 2 |
| #31826686 | 2 |
| #31826674 | 2 |
| #31826664 | 2 |
| #31826488 | 2 |
| #31826464 | 2 |
| #417×C283 | 2 |
| #3037 | 283 |