Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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×M16×C23 | C2 | semidirect |
| 3. C2×C4×Dic23 | C2 | semidirect |
| 4. #10625007 | C2 | direct (N × H) |
| 10. #67288 | C4 | semidirect |
| 12. C2×D92 | C4 | semidirect |
| 14. C2×Dic46 | C4 | semidirect |
| 16. M16×C23 | C22 | semidirect |
| 19. C4×Dic23 | C22 | semidirect |
| 34. D92 | C2×C4 | semidirect |
| 38. Dic46 | C2×C4 | semidirect |
| 55. C2×C23 | #104 | semidirect |
| 59. C2×M16 | D23 | semidirect |
| 62. C23 | C2×#104 | semidirect |
| 74. M16 | C2×D23 | semidirect |
| 113. C2 | #10625007 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67288 | 2 |
| C2×M16×C23 | 2 |
| C2×C4×Dic23 | 2 |
| #10625007 | 2 |
| C2×#104 | 23 |