Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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×#20300222 | C2 | semidirect |
| 3. #28408837 | C2 | semidirect |
| 4. #28408834 | C2 | semidirect |
| 5. C2×M32×C227 | C2 | semidirect |
| 8. #20300310 | C4 | semidirect |
| 26. Dic908 | C2×C4 | semidirect |
| 29. D1816 | C2×C4 | semidirect |
| 73. C227 | #2139 | semidirect |
| 76. C2×M32 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300310 | 2 |
| C2×#20300222 | 2 |
| #28408837 | 2 |
| #28408834 | 2 |
| C2×M32×C227 | 2 |
| #2139 | 227 |