Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 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. #28409088 | C2 | direct (N × H) |
| 3. C2×C4⋊(C227⋊C8) | C2 | semidirect |
| 5. C2×#20300198 | C2 | semidirect |
| 6. C2×C4⋊C8×C227 | C2 | semidirect |
| 16. C4⋊(C227⋊C8) | C22 | semidirect |
| 18. #20300198 | C22 | semidirect |
| 21. C4⋊C8×C227 | C22 | semidirect |
| 89. C2×C227 | #432 | semidirect |
| 94. C227 | C2×#432 | semidirect |
| 99. C2×C4⋊C8 | D227 | semidirect |
| 114. C4⋊C8 | C2×D227 | semidirect |
| 185. C2 | #28409088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D227 | 2 |
| #28409088 | 2 |
| C2×C4⋊(C227⋊C8) | 2 |
| C2×(C2×D227)⋊C8 | 2 |
| C2×#20300198 | 2 |
| C2×C4⋊C8×C227 | 2 |
| C2×#432 | 227 |