Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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×#20300234 | C2 | semidirect |
| 4. C4⋊(C227⋊C16) | C2 | semidirect |
| 5. #28408835 | C2 | semidirect |
| 7. C4×Q16×C227 | C2 | semidirect |
| 72. C227 | #2211 | semidirect |
| 77. C4×Q16 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300234 | 2 |
| C2×#20300231 | 2 |
| #28409416 | 2 |
| C4⋊(C227⋊C16) | 2 |
| #28408835 | 2 |
| #28408832 | 2 |
| C4×Q16×C227 | 2 |
| #2211 | 227 |