Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D23 | C2 | semidirect |
| 3. C2×#10625117 | C2 | semidirect |
| 4. #13092672 | C2 | semidirect |
| 5. #13092660 | C2 | semidirect |
| 6. #13092655 | C2 | semidirect |
| 7. #13092643 | C2 | semidirect |
| 8. #13092459 | C2 | semidirect |
| 9. #13092426 | C2 | semidirect |
| 10. #13092418 | C2 | semidirect |
| 11. C2×C23×#137 | C2 | semidirect |
| 16. C2×Q16×C23 | C22 | semidirect |
| 17. C2×SD16×C23 | C22 | semidirect |
| 39. #10625017 | C22 | semidirect |
| 40. #10625017 | C22 | semidirect |
| 41. #10625017 | C22 | semidirect |
| 42. #10625014 | C22 | semidirect |
| 43. #10625000 | C22 | semidirect |
| 44. #10624999 | C22 | semidirect |
| 70. M16×C23 | D4 | semidirect |
| 146. C2×D23 | #137 | semidirect |
| 157. C2×#137 | D23 | semidirect |
| 179. C2×Q16 | C2×D23 | semidirect |
| 180. C2×SD16 | C2×D23 | semidirect |
| 208. C23 | #3056 | semidirect |
| 236. M16 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D23 | 2 |
| #13092924 | 2 |
| C2×#10625117 | 2 |
| #13092672 | 2 |
| #13092660 | 2 |
| #13092655 | 2 |
| #13092643 | 2 |
| #13092459 | 2 |
| #13092426 | 2 |
| #13092418 | 2 |
| C2×C23×#137 | 2 |
| #3056 | 23 |