Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
130 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 130 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×#121 | C2 | semidirect |
| 2. C2×#67272 | C2 | semidirect |
| 3. #10625101 | C2 | semidirect |
| 4. C2×#67267 | C2 | semidirect |
| 5. #10625014 | C2 | semidirect |
| 6. #10624991 | C2 | semidirect |
| 7. #10624990 | C2 | semidirect |
| 37. C23⋊C8 | D4 | semidirect |
| 63. #121 | D23 | semidirect |
| 67. C23 | #469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#121 | 2 |
| C2×#67272 | 2 |
| #10625101 | 2 |
| C2×#67267 | 2 |
| #10625014 | 2 |
| #10624991 | 2 |
| #10624990 | 2 |
| #469 | 23 |