Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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. Q8×#13181884 | C2 | semidirect |
| 3. #28357289 | C2 | semidirect |
| 4. #28357283 | C2 | semidirect |
| 6. #28357274 | C2 | semidirect |
| 18. #20294086 | C4 | semidirect |
| 19. #20294085 | C4 | semidirect |
| 20. #20294084 | C4 | semidirect |
| 22. SD16×C433 | C4 | semidirect |
| 31. Dic866 | C2×C4 | semidirect |
| 36. #16812358 | C2×C4 | semidirect |
| 37. Q8×C433 | C2×C4 | semidirect |
| 39. C8×C433 | C2×C4 | semidirect |
| 58. C433 | #440 | semidirect |
| 73. SD16 | #13181884 | semidirect |
| 85. Q8 | C2×#13181884 | semidirect |
| 98. C8 | C2×#13181884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13181884 | 2 |
| D4×#13181884 | 2 |
| #28357289 | 2 |
| #28357283 | 2 |
| #28357282 | 2 |
| #28357274 | 2 |
| SD16×D433 | 2 |
| #440 | 433 |