Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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. #28409747 | C2 | semidirect |
| 2. #28409405 | C2 | semidirect |
| 3. #28409228 | C2 | semidirect |
| 4. #28409227 | C2 | semidirect |
| 5. #28408780 | C2 | semidirect |
| 6. #28408761 | C2 | semidirect |
| 7. D4⋊C8×C227 | C2 | semidirect |
| 101. C227 | #1624 | semidirect |
| 109. D4⋊C8 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28409747 | 2 |
| #28409405 | 2 |
| #28409228 | 2 |
| #28409227 | 2 |
| #28408780 | 2 |
| #28408761 | 2 |
| D4⋊C8×C227 | 2 |
| #1624 | 227 |