Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 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. C22×#67263 | C2 | semidirect |
| 2. #13092988 | C2 | semidirect |
| 4. #13092663 | C2 | semidirect |
| 5. #13092646 | C2 | semidirect |
| 6. #13092455 | C2 | semidirect |
| 7. #13092427 | C2 | semidirect |
| 8. #13092423 | C2 | semidirect |
| 9. C2×C23×#131 | C2 | semidirect |
| 15. C2×M16×C23 | C22 | semidirect |
| 17. C22×C8×C23 | C22 | semidirect |
| 27. #10625095 | C22 | semidirect |
| 32. #10625000 | C22 | semidirect |
| 33. #10624999 | C22 | semidirect |
| 34. #10624998 | C22 | semidirect |
| 56. C2×C8×C23 | D4 | semidirect |
| 117. C2×#131 | D23 | semidirect |
| 138. C2×M16 | C2×D23 | semidirect |
| 140. C22×C8 | C2×D23 | semidirect |
| 155. C23 | #3057 | semidirect |
| 179. C2×C8 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67263 | 2 |
| #13092988 | 2 |
| #13092981 | 2 |
| #13092663 | 2 |
| #13092646 | 2 |
| #13092455 | 2 |
| #13092427 | 2 |
| #13092423 | 2 |
| C2×C23×#131 | 2 |
| #3057 | 23 |