Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 3. #31826872 | C2 | semidirect |
| 4. #31826870 | C2 | semidirect |
| 5. #31826868 | C2 | semidirect |
| 6. #31826861 | C2 | semidirect |
| 9. #498×C283 | C2 | semidirect |
| 43. #17985375 | Q8 | semidirect |
| 79. C283⋊C8 | C2×Q8 | semidirect |
| 87. C8×C283 | C2×Q8 | semidirect |
| 106. C283 | #3165 | semidirect |
| 114. #498 | D283 | semidirect |
| 194. C8 | Q8×D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827020 | 2 |
| C4⋊Q8×D283 | 2 |
| #31826872 | 2 |
| #31826870 | 2 |
| #31826868 | 2 |
| #31826861 | 2 |
| #31826504 | 2 |
| C4×#17985375 | 2 |
| #498×C283 | 2 |
| #3165 | 283 |