Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #31826933 | C2 | semidirect |
| 3. #31826481 | C2 | semidirect |
| 4. C2×#22583536 | C2 | semidirect |
| 5. #31826438 | C2 | semidirect |
| 6. #31826226 | C2 | semidirect |
| 7. #344×C283 | C2 | semidirect |
| 11. #22583643 | C4 | semidirect |
| 13. #22583638 | C4 | semidirect |
| 37. C2×Dic566 | C2×C4 | semidirect |
| 39. C2×D1132 | C2×C4 | semidirect |
| 64. M16×C283 | C2×C4 | semidirect |
| 129. C283 | #1906 | semidirect |
| 136. #344 | D283 | semidirect |
| 185. M16 | C4×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827265 | 2 |
| #31826933 | 2 |
| #31826481 | 2 |
| C2×#22583536 | 2 |
| #31826438 | 2 |
| #31826226 | 2 |
| #344×C283 | 2 |
| #1906 | 283 |