Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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. #10625119 | C2 | semidirect |
| 3. #10625078 | C2 | semidirect |
| 4. C23×#104 | C2 | semidirect |
| 5. #10625004 | C2 | semidirect |
| 6. #10624987 | C2 | semidirect |
| 7. C4×C23⋊C8 | C2 | semidirect |
| 12. #67275 | C4 | semidirect |
| 13. #67274 | C4 | semidirect |
| 14. #67273 | C4 | semidirect |
| 15. #67272 | C4 | semidirect |
| 57. #104 | D23 | semidirect |
| 59. C23 | #443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10625121 | 2 |
| #10625119 | 2 |
| #10625078 | 2 |
| C23×#104 | 2 |
| #10625004 | 2 |
| #10624987 | 2 |
| C4×C23⋊C8 | 2 |
| #443 | 23 |