Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×Q8×D431 | C2 | semidirect |
| 3. #28352187 | C2 | semidirect |
| 4. #28352178 | C2 | semidirect |
| 5. #28352177 | C2 | semidirect |
| 6. #28352174 | C2 | semidirect |
| 7. #28352167 | C2 | semidirect |
| 8. #28352146 | C2 | semidirect |
| 9. C4⋊Q8×C431 | C2 | semidirect |
| 63. C431 | #536 | semidirect |
| 68. C4⋊Q8 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293801 | 2 |
| C2×Q8×D431 | 2 |
| #28352187 | 2 |
| #28352178 | 2 |
| #28352177 | 2 |
| #28352174 | 2 |
| #28352167 | 2 |
| #28352146 | 2 |
| C4⋊Q8×C431 | 2 |
| #536 | 431 |