Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 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. C2×#20300231 | C2 | semidirect |
| 2. C2×#20300229 | C2 | semidirect |
| 3. #28409268 | C2 | semidirect |
| 4. #28408836 | C2 | semidirect |
| 5. #28408833 | C2 | semidirect |
| 6. C22⋊(C227⋊C16) | C2 | semidirect |
| 7. C2×#135×C227 | C2 | semidirect |
| 39. Q16×C227 | D4 | semidirect |
| 42. D8×C227 | D4 | semidirect |
| 89. C227 | #2186 | semidirect |
| 91. C2×#135 | D227 | semidirect |
| 123. Q16 | C22⋊D227 | semidirect |
| 128. D8 | C22⋊D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300231 | 2 |
| C2×#20300229 | 2 |
| #28409268 | 2 |
| #28408836 | 2 |
| #28408833 | 2 |
| C22⋊(C227⋊C16) | 2 |
| C2×#135×C227 | 2 |
| #2186 | 227 |