Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 189 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. C2×#20300276 | C2 | semidirect |
| 2. C2×#20300267 | C2 | semidirect |
| 4. #28408938 | C2 | semidirect |
| 5. #28408934 | C2 | semidirect |
| 6. #28408923 | C2 | semidirect |
| 7. #28408911 | C2 | semidirect |
| 8. #28408898 | C2 | semidirect |
| 9. C22×C42×C227 | C2 | semidirect |
| 63. C42×C227 | D4 | semidirect |
| 103. C22×C227 | #124 | semidirect |
| 128. C227 | #2850 | semidirect |
| 133. C22×C42 | D227 | semidirect |
| 192. C42 | C22⋊D227 | semidirect |
| 237. C22 | #20300276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20300276 | 2 |
| C2×#20300267 | 2 |
| C2×#20300262 | 2 |
| #28408938 | 2 |
| #28408934 | 2 |
| #28408923 | 2 |
| #28408911 | 2 |
| #28408898 | 2 |
| C22×C42×C227 | 2 |
| #2850 | 227 |