Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
170 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4×Dic23 | C2 | semidirect |
| 3. C2×#67267 | C2 | semidirect |
| 4. #10625019 | C2 | direct (N × H) |
| 7. #41×C23 | C4 | semidirect |
| 9. C2×Q8×C23 | C4 | semidirect |
| 11. C2×D4×C23 | C4 | semidirect |
| 16. C4×Dic23 | C22 | semidirect |
| 18. #67267 | C22 | semidirect |
| 23. Q8×C23 | C2×C4 | semidirect |
| 27. D4×C23 | C2×C4 | semidirect |
| 56. C2×C23 | #104 | semidirect |
| 62. C23 | C2×#104 | semidirect |
| 65. #41 | Dic23 | semidirect |
| 67. C2×Q8 | Dic23 | semidirect |
| 69. C2×D4 | Dic23 | semidirect |
| 81. Q8 | C2×Dic23 | semidirect |
| 85. D4 | C2×Dic23 | semidirect |
| 113. C2 | #10625019 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C23 | 2 |
| C2×C4×Dic23 | 2 |
| C2×#67267 | 2 |
| #10625019 | 2 |
| C2×#104 | 23 |