Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 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×#10625079 | C2 | semidirect |
| 2. #13092995 | C2 | semidirect |
| 3. #13092981 | C2 | semidirect |
| 4. #13092670 | C2 | semidirect |
| 5. #13092663 | C2 | semidirect |
| 6. #13092653 | C2 | semidirect |
| 7. #13092646 | C2 | semidirect |
| 8. #13092459 | C2 | semidirect |
| 9. #13092414 | C2 | semidirect |
| 10. C2×#10625003 | C2 | semidirect |
| 11. C2×C23×#131 | C2 | semidirect |
| 17. C2×M16×C23 | C22 | semidirect |
| 19. C22×C8×C23 | C22 | semidirect |
| 28. #10625101 | C22 | semidirect |
| 31. #10625095 | C22 | semidirect |
| 37. #10625003 | C22 | semidirect |
| 38. #10625003 | C22 | semidirect |
| 39. #10625000 | C22 | semidirect |
| 40. #10624999 | C22 | semidirect |
| 41. #10624998 | C22 | semidirect |
| 42. #10624998 | C22 | semidirect |
| 66. M16×C23 | D4 | semidirect |
| 146. C2×#131 | D23 | semidirect |
| 171. C2×M16 | C2×D23 | semidirect |
| 173. C22×C8 | C2×D23 | semidirect |
| 194. C23 | #3062 | semidirect |
| 220. M16 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625079 | 2 |
| #13092995 | 2 |
| #13092981 | 2 |
| #13092670 | 2 |
| #13092663 | 2 |
| #13092653 | 2 |
| #13092646 | 2 |
| #13092459 | 2 |
| #13092414 | 2 |
| C2×#10625003 | 2 |
| C2×C23×#131 | 2 |
| #3062 | 23 |