Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
258 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q16×C23 | C2 | semidirect |
| 4. C2×#67275 | C2 | semidirect |
| 5. C2×#67274 | C2 | semidirect |
| 6. #10625089 | C2 | direct (N × H) |
| 7. C2×#67263 | C2 | semidirect |
| 8. C2×#67262 | C2 | semidirect |
| 14. Q8×D23 | C22 | semidirect |
| 22. Q16×C23 | C22 | semidirect |
| 24. #67275 | C22 | semidirect |
| 25. #67274 | C22 | semidirect |
| 27. #67263 | C22 | semidirect |
| 28. #67262 | C22 | semidirect |
| 64. C2×C23 | #137 | semidirect |
| 72. C2×Q16 | D23 | semidirect |
| 76. C23 | C2×#137 | semidirect |
| 91. Q16 | C2×D23 | semidirect |
| 133. C2 | #10625089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67292 | 2 |
| C2×Q8×D23 | 2 |
| C2×Q16×C23 | 2 |
| C2×#67275 | 2 |
| C2×#67274 | 2 |
| #10625089 | 2 |
| C2×#67263 | 2 |
| C2×#67262 | 2 |
| C2×#137 | 23 |