Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
572 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10625122 | C2 | semidirect |
| 2. C2×#10625120 | C2 | semidirect |
| 3. C2×#10625046 | C2 | semidirect |
| 4. #13092809 | C2 | semidirect |
| 5. #13092804 | C2 | semidirect |
| 6. #13092799 | C2 | semidirect |
| 7. C4×#67267 | C2 | semidirect |
| 8. C23×#532 | C2 | semidirect |
| 12. C23×C4⋊Q8 | C22 | semidirect |
| 13. C23×#127 | C22 | semidirect |
| 14. C23×#124 | C22 | semidirect |
| 20. C2×#67275 | C22 | semidirect |
| 22. C2×#67273 | C22 | semidirect |
| 29. #10624985 | C22 | semidirect |
| 30. C4×C23⋊C8 | C22 | semidirect |
| 59. #67267 | D4 | semidirect |
| 104. #532 | D23 | semidirect |
| 125. C4⋊Q8 | C2×D23 | semidirect |
| 126. #127 | C2×D23 | semidirect |
| 130. #124 | C2×D23 | semidirect |
| 137. C23 | #3153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625122 | 2 |
| C2×#10625120 | 2 |
| C2×#10625046 | 2 |
| #13092809 | 2 |
| #13092804 | 2 |
| #13092799 | 2 |
| C4×#67267 | 2 |
| C23×#532 | 2 |
| #3153 | 23 |