Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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. #28352188 | C2 | semidirect |
| 2. #28352187 | C2 | semidirect |
| 3. #28352179 | C2 | semidirect |
| 6. Q8×Dic431 | C2 | semidirect |
| 7. #28352154 | C2 | semidirect |
| 8. #28352154 | C2 | semidirect |
| 38. C2×Dic431 | Q8 | semidirect |
| 70. C431 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352188 | 2 |
| #28352187 | 2 |
| #28352179 | 2 |
| #28352168 | 2 |
| #28352166 | 2 |
| Q8×Dic431 | 2 |
| #28352154 | 2 |
| #28352145 | 2 |
| C2×C4×Dic431 | 2 |
| C22⋊Q8×C431 | 2 |
| #533 | 431 |