Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#20293799 | C2 | semidirect |
| 2. C2×#20293788 | C2 | semidirect |
| 3. #28352160 | C2 | semidirect |
| 4. #28352114 | C2 | semidirect |
| 5. #28352110 | C2 | semidirect |
| 6. (C2×D431)⋊C8 | C2 | semidirect |
| 7. C2×D8×C431 | C2 | semidirect |
| 25. Dic862 | D4 | semidirect |
| 40. D4×C431 | D4 | semidirect |
| 64. C431 | #449 | semidirect |
| 68. C2×D8 | D431 | semidirect |
| 98. D4 | C22⋊D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293799 | 2 |
| C2×#20293788 | 2 |
| #28352160 | 2 |
| #28352114 | 2 |
| #28352110 | 2 |
| (C2×D431)⋊C8 | 2 |
| C2×D8×C431 | 2 |
| #449 | 431 |