Finite Group DatabasebetaFinite Group DatabasebetaOrder 29056.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. Q8×D908 | C2 | semidirect |
| 2. #28409379 | C2 | semidirect |
| 3. #28409232 | C2 | semidirect |
| 5. #28408777 | C2 | semidirect |
| 6. #28408761 | C2 | semidirect |
| 7. Q8⋊C8×C227 | C2 | semidirect |
| 62. D908 | SD16 | semidirect |
| 70. Q8×C227 | D8 | semidirect |
| 99. C227 | #1627 | semidirect |
| 106. Q8⋊C8 | D227 | semidirect |
| 157. Q8 | D1816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D908 | 2 |
| #28409379 | 2 |
| #28409232 | 2 |
| #28409228 | 2 |
| #28408777 | 2 |
| #28408761 | 2 |
| Q8⋊C8×C227 | 2 |
| #1627 | 227 |