Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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. C23×#117 | C2 | semidirect |
| 3. #10625097 | C2 | semidirect |
| 4. #10625063 | C2 | semidirect |
| 5. C4⋊C4×D23 | C2 | semidirect |
| 7. #10625048 | C2 | semidirect |
| 8. #10625043 | C2 | semidirect |
| 9. C42×D23 | C2 | semidirect |
| 13. C2×C4×D23 | C4 | semidirect |
| 19. C4⋊C4×C23 | C22 | semidirect |
| 21. C42×C23 | C22 | semidirect |
| 24. C4⋊Dic23 | C22 | semidirect |
| 25. Dic23⋊C4 | C22 | semidirect |
| 26. C4×Dic23 | C22 | semidirect |
| 27. C4×Dic23 | C22 | semidirect |
| 33. C2×C4×C23 | C2×C4 | semidirect |
| 37. C2×Dic23 | C2×C4 | semidirect |
| 44. C4×D23 | C2×C4 | semidirect |
| 45. C4×D23 | C2×C4 | semidirect |
| 65. D23 | #117 | direct (N × H) |
| 71. #117 | D23 | direct (N × H) |
| 75. C23 | C2×#117 | semidirect |
| 87. C4⋊C4 | C2×D23 | semidirect |
| 93. C42 | C2×D23 | semidirect |
| 108. C2×C4 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D23 | 2 |
| C23×#117 | 2 |
| #10625097 | 2 |
| #10625063 | 2 |
| C4⋊C4×D23 | 2 |
| C22⋊C4×D23 | 2 |
| #10625048 | 2 |
| #10625043 | 2 |
| C42×D23 | 2 |
| C2×#117 | 23 |