Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. C22×Q8×C23 | C2 | semidirect |
| 3. #10625117 | C2 | direct (N × H) |
| 5. C2×C4⋊Dic23 | C2 | semidirect |
| 6. C2×Dic23⋊C4 | C2 | semidirect |
| 9. C2×Q8×C23 | C22 | semidirect |
| 17. C4⋊Dic23 | C22 | semidirect |
| 18. Dic23⋊C4 | C22 | semidirect |
| 22. C22×D23 | Q8 | semidirect |
| 41. C2×D23 | C2×Q8 | semidirect |
| 47. C2×C23 | C22⋊Q8 | semidirect |
| 52. C22×Q8 | D23 | semidirect |
| 58. C23 | C2×C22⋊Q8 | semidirect |
| 61. C2×Q8 | C2×D23 | semidirect |
| 99. C2 | #10625117 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×C23 | 2 |
| C22×C4×D23 | 2 |
| #10625117 | 2 |
| C2×(C2×D23)⋊C4 | 2 |
| C2×C4⋊Dic23 | 2 |
| C2×Dic23⋊C4 | 2 |
| C2×C22⋊Q8 | 23 |