Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. C23×C22⋊Q8 | C2 | semidirect |
| 2. C2×#67274 | C2 | semidirect |
| 4. C2×#67267 | C2 | semidirect |
| 5. #10625017 | C2 | semidirect |
| 6. #10624991 | C2 | semidirect |
| 7. #10624989 | C2 | semidirect |
| 36. C23⋊C8 | D4 | semidirect |
| 58. C22⋊Q8 | D23 | semidirect |
| 63. C23 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊Q8 | 2 |
| C2×#67274 | 2 |
| #10625101 | 2 |
| C2×#67267 | 2 |
| #10625017 | 2 |
| #10624991 | 2 |
| #10624989 | 2 |
| #468 | 23 |