Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 124 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. C2×#20294080 | C2 | semidirect |
| 2. C2×C8×D433 | C2 | semidirect |
| 4. C4⋊#16812358 | C2 | semidirect |
| 5. #28357132 | C2 | semidirect |
| 6. #28357132 | C2 | semidirect |
| 7. #97×C433 | C2 | semidirect |
| 36. C8×C433 | D4 | semidirect |
| 43. C2×D433 | M16 | semidirect |
| 55. C433 | #435 | semidirect |
| 63. #97 | D433 | semidirect |
| 92. C8 | D1732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294080 | 2 |
| C2×C8×D433 | 2 |
| C4×D1732 | 2 |
| C4⋊#16812358 | 2 |
| #28357132 | 2 |
| #97×C433 | 2 |
| #435 | 433 |