Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#67274 | C2 | semidirect |
| 2. C2×#10625119 | C2 | semidirect |
| 4. #13092665 | C2 | semidirect |
| 5. #13092648 | C2 | semidirect |
| 6. #13092453 | C2 | semidirect |
| 7. #13092426 | C2 | semidirect |
| 8. #13092421 | C2 | semidirect |
| 9. C23×#536 | C2 | semidirect |
| 16. C23×C22⋊Q8 | C22 | semidirect |
| 28. C2×#67267 | C22 | semidirect |
| 30. C22×C23⋊C8 | C22 | semidirect |
| 31. #10625017 | C22 | semidirect |
| 33. #10624990 | C22 | semidirect |
| 34. #10624989 | C22 | semidirect |
| 67. C2×C23⋊C8 | D4 | semidirect |
| 118. #536 | D23 | semidirect |
| 146. C22⋊Q8 | C2×D23 | semidirect |
| 155. C23 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67274 | 2 |
| C2×#10625119 | 2 |
| #13092981 | 2 |
| #13092665 | 2 |
| #13092648 | 2 |
| #13092453 | 2 |
| #13092426 | 2 |
| #13092421 | 2 |
| C23×#536 | 2 |
| #3057 | 23 |