Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
452 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 217 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. #28409110 | C2 | semidirect |
| 2. #28409085 | C2 | semidirect |
| 3. #28408996 | C2 | semidirect |
| 5. C2×#16813868 | C22 | semidirect |
| 6. C4⋊(C227⋊C8) | C22 | semidirect |
| 8. C22⋊(C227⋊C8) | C22 | semidirect |
| 9. C4×C227⋊C8 | C22 | semidirect |
| 45. C2×C4×C227 | M16 | semidirect |
| 69. C227 | #2975 | semidirect |
| 114. C2×C4 | #16813868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409110 | 2 |
| #28409085 | 2 |
| #28408996 | 2 |
| C2×C4×D4×C227 | 2 |
| #2975 | 227 |