Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 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. #10625017 | C2 | semidirect |
| 5. #10625014 | C2 | semidirect |
| 7. #41×C23 | C4 | semidirect |
| 21. Q8×C23 | C2×C4 | semidirect |
| 24. D4×C23 | C2×C4 | semidirect |
| 57. C23 | #417 | semidirect |
| 59. #41 | Dic23 | semidirect |
| 73. Q8 | C2×Dic23 | semidirect |
| 76. D4 | C2×Dic23 | semidirect |
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 |
| #10625017 | 2 |
| #10625014 | 2 |
| #417 | 23 |