Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
278 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31827137 | C2 | semidirect |
| 2. #31826841 | C2 | semidirect |
| 3. #31826657 | C2 | semidirect |
| 4. #31826208 | C2 | semidirect |
| 5. Q8⋊(C283⋊C8) | C2 | semidirect |
| 6. #31826192 | C2 | semidirect |
| 7. #460×C283 | C2 | semidirect |
| 71. Q8×C283 | D8 | semidirect |
| 107. C283 | #1621 | semidirect |
| 111. #460 | D283 | semidirect |
| 164. Q8 | #17985377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827137 | 2 |
| #31826841 | 2 |
| #31826657 | 2 |
| #31826208 | 2 |
| Q8⋊(C283⋊C8) | 2 |
| #31826192 | 2 |
| #460×C283 | 2 |
| #1621 | 283 |