Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #28409140 | C2 | semidirect |
| 4. #28409139 | C2 | semidirect |
| 5. #28409138 | C2 | semidirect |
| 6. C4×#16813874 | C2 | semidirect |
| 7. #28409124 | C2 | semidirect |
| 11. #441×C227 | C2 | semidirect |
| 15. Q16×D227 | C4 | semidirect |
| 108. C227 | #2950 | semidirect |
| 115. #441 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D227 | 2 |
| #28409508 | 2 |
| #28409140 | 2 |
| #28409139 | 2 |
| #28409138 | 2 |
| C4×#16813874 | 2 |
| #28409124 | 2 |
| #28409067 | 2 |
| #28409039 | 2 |
| #28408989 | 2 |
| #441×C227 | 2 |
| #2950 | 227 |