Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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×D4×D23 | C2 | semidirect |
| 2. C2×D8×C23 | C2 | semidirect |
| 3. #10625109 | C2 | semidirect |
| 4. C2×#67272 | C2 | semidirect |
| 5. #10625014 | C2 | semidirect |
| 6. #10625003 | C2 | semidirect |
| 7. (C2×D23)⋊C8 | C2 | semidirect |
| 10. C2×D4×C23 | C22 | semidirect |
| 18. C2×C8×C23 | C22 | semidirect |
| 21. C4⋊Dic23 | C22 | semidirect |
| 22. C2×C23⋊C8 | C22 | semidirect |
| 33. D4×C23 | D4 | semidirect |
| 40. D92 | D4 | semidirect |
| 58. C2×D23 | D8 | semidirect |
| 73. C2×D8 | D23 | semidirect |
| 78. C23 | #447 | semidirect |
| 86. C2×D4 | C2×D23 | semidirect |
| 91. C2×C8 | C2×D23 | semidirect |
| 108. D4 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D23 | 2 |
| C2×D8×C23 | 2 |
| #10625109 | 2 |
| C2×#67272 | 2 |
| #10625014 | 2 |
| #10625003 | 2 |
| (C2×D23)⋊C8 | 2 |
| #447 | 23 |