Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
376 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#20300219 | C2 | semidirect |
| 3. C2×#20300210 | C2 | semidirect |
| 4. C2×#20300198 | C2 | semidirect |
| 5. #28408935 | C2 | semidirect |
| 6. #28408933 | C2 | semidirect |
| 7. C2×#102×C227 | C2 | semidirect |
| 11. C2×#16813869 | C4 | semidirect |
| 71. C227⋊C8 | C22⋊C4 | semidirect |
| 120. C227 | #1972 | semidirect |
| 125. C2×#102 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16813869 | 2 |
| C2×#20300219 | 2 |
| C2×#20300210 | 2 |
| C2×#20300198 | 2 |
| #28408935 | 2 |
| #28408933 | 2 |
| C2×#102×C227 | 2 |
| #1972 | 227 |