Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 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. C2×#67273 | C2 | semidirect |
| 3. C2×#67263 | C2 | semidirect |
| 4. #10625068 | C2 | semidirect |
| 5. C23×#102 | C2 | semidirect |
| 6. (C2×D23)⋊C8 | C2 | semidirect |
| 7. #10624991 | C2 | semidirect |
| 15. C2×Dic46 | C22 | semidirect |
| 16. C2×C8×C23 | C22 | semidirect |
| 17. C4⋊C4×C23 | C22 | semidirect |
| 21. C2×C23⋊C8 | C22 | semidirect |
| 54. C2×D23 | SD16 | semidirect |
| 72. #102 | D23 | semidirect |
| 74. C23 | #450 | semidirect |
| 86. C2×C8 | C2×D23 | semidirect |
| 88. C4⋊C4 | C2×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D23 | 2 |
| C2×#67273 | 2 |
| C2×#67263 | 2 |
| #10625068 | 2 |
| C23×#102 | 2 |
| (C2×D23)⋊C8 | 2 |
| #10624991 | 2 |
| #450 | 23 |