Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#67288 | C2 | semidirect |
| 2. C23×#121 | C2 | semidirect |
| 3. C2×#67273 | C2 | semidirect |
| 4. C2×#67272 | C2 | semidirect |
| 5. C22⋊(C23⋊C8) | C2 | semidirect |
| 6. #10624992 | C2 | semidirect |
| 7. #10624991 | C2 | semidirect |
| 37. D92 | D4 | semidirect |
| 40. Dic46 | D4 | semidirect |
| 68. #121 | D23 | semidirect |
| 72. C23 | #449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67288 | 2 |
| C23×#121 | 2 |
| C2×#67273 | 2 |
| C2×#67272 | 2 |
| C22⋊(C23⋊C8) | 2 |
| #10624992 | 2 |
| #10624991 | 2 |
| #449 | 23 |