Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #31827265 | C2 | semidirect |
| 2. C2×#22583638 | C2 | semidirect |
| 3. #31827034 | C2 | semidirect |
| 4. #31826481 | C2 | semidirect |
| 5. #31826471 | C2 | semidirect |
| 6. #31826438 | C2 | semidirect |
| 7. #344×C283 | C2 | semidirect |
| 41. C2×Dic566 | D4 | semidirect |
| 50. C2×D1132 | D4 | semidirect |
| 69. M16×C283 | D4 | semidirect |
| 71. C2×C8×C283 | D4 | semidirect |
| 142. C283 | #2008 | semidirect |
| 150. #344 | D283 | semidirect |
| 208. M16 | D1132 | semidirect |
| 210. C2×C8 | D1132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827265 | 2 |
| C2×#22583638 | 2 |
| #31827034 | 2 |
| #31826481 | 2 |
| #31826471 | 2 |
| #31826438 | 2 |
| #344×C283 | 2 |
| #2008 | 283 |