Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C2×Q8×D23 | C2 | semidirect |
| 3. C23×#137 | C2 | semidirect |
| 4. #10625122 | C2 | semidirect |
| 5. #10625113 | C2 | semidirect |
| 6. #10625089 | C2 | semidirect |
| 7. Q16×D23 | C2 | semidirect |
| 8. #10625086 | C2 | semidirect |
| 9. SD16×D23 | C2 | semidirect |
| 10. #10625080 | C2 | semidirect |
| 11. M16×D23 | C2 | semidirect |
| 13. C2×Q8×C23 | C22 | semidirect |
| 19. Q8×D23 | C22 | semidirect |
| 30. C2×Dic46 | C22 | semidirect |
| 31. Q16×C23 | C22 | semidirect |
| 32. SD16×C23 | C22 | semidirect |
| 33. M16×C23 | C22 | semidirect |
| 34. #67275 | C22 | semidirect |
| 35. #67275 | C22 | semidirect |
| 36. #67274 | C22 | semidirect |
| 37. #67273 | C22 | semidirect |
| 38. #67267 | C22 | semidirect |
| 39. Dic92 | C22 | semidirect |
| 40. #67263 | C22 | semidirect |
| 41. #67262 | C22 | semidirect |
| 99. D23 | #137 | direct (N × H) |
| 107. #137 | D23 | direct (N × H) |
| 111. C23 | C2×#137 | semidirect |
| 125. C2×Q8 | C2×D23 | semidirect |
| 134. Q16 | C2×D23 | semidirect |
| 138. SD16 | C2×D23 | semidirect |
| 141. M16 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D23 | 2 |
| C2×Q8×D23 | 2 |
| C23×#137 | 2 |
| #10625122 | 2 |
| #10625113 | 2 |
| #10625089 | 2 |
| Q16×D23 | 2 |
| #10625086 | 2 |
| SD16×D23 | 2 |
| #10625080 | 2 |
| M16×D23 | 2 |
| C2×#137 | 23 |