Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
426 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×D1732 | C2 | semidirect |
| 2. C22×C22⋊D433 | C2 | semidirect |
| 3. C22×C22⋊D433 | C2 | semidirect |
| 4. C22×C4×D433 | C2 | semidirect |
| 5. #28357193 | C2 | direct (N × H) |
| 6. C2×#20294076 | C2 | semidirect |
| 7. C2×#20294074 | C2 | semidirect |
| 8. C2×C22⋊C4×C433 | C2 | semidirect |
| 12. C2×D1732 | C22 | semidirect |
| 15. C2×C22⋊D433 | C22 | semidirect |
| 16. C2×C22⋊D433 | C22 | semidirect |
| 20. C2×C4×D433 | C22 | semidirect |
| 21. #20294076 | C22 | semidirect |
| 22. #20294074 | C22 | semidirect |
| 26. C22⋊C4×C433 | C22 | semidirect |
| 32. C22×D433 | D4 | semidirect |
| 39. C2×Dic433 | D4 | semidirect |
| 67. C2×D433 | C2×D4 | semidirect |
| 71. Dic433 | C2×D4 | semidirect |
| 73. C2×C433 | #121 | semidirect |
| 79. C433 | C2×#121 | semidirect |
| 88. C2×C22⋊C4 | D433 | semidirect |
| 106. C22⋊C4 | C2×D433 | semidirect |
| 155. C2 | #28357193 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1732 | 2 |
| C22×C22⋊D433 | 2 |
| C22×C4×D433 | 2 |
| #28357193 | 2 |
| C2×#20294076 | 2 |
| C2×#20294074 | 2 |
| C2×C22⋊C4×C433 | 2 |
| C2×#121 | 433 |