Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
340 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 79 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. #28409798 | C2 | semidirect |
| 3. #28409014 | C2 | semidirect |
| 4. C2×#20300205 | C2 | semidirect |
| 5. #28408804 | C2 | semidirect |
| 6. #28408803 | C2 | semidirect |
| 7. C2×#100×C227 | C2 | semidirect |
| 38. #16813868 | D4 | semidirect |
| 58. M16×C227 | D4 | semidirect |
| 114. C227 | #1914 | semidirect |
| 120. C2×#100 | D227 | semidirect |
| 166. M16 | C22⋊D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409798 | 2 |
| #28409599 | 2 |
| #28409014 | 2 |
| C2×#20300205 | 2 |
| #28408804 | 2 |
| #28408803 | 2 |
| C2×#100×C227 | 2 |
| #1914 | 227 |