Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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. #28409384 | C2 | semidirect |
| 2. #28409327 | C2 | semidirect |
| 4. #28408778 | C2 | semidirect |
| 5. Q8⋊(C227⋊C8) | C2 | semidirect |
| 90. C227 | #1637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409384 | 2 |
| #28409327 | 2 |
| #28409322 | 2 |
| #28408778 | 2 |
| Q8⋊(C227⋊C8) | 2 |
| D4⋊(C227⋊C8) | 2 |
| D4×Q8×C227 | 2 |
| #1637 | 227 |