Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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×#10625080 | C2 | semidirect |
| 2. C2×#10625113 | C2 | semidirect |
| 3. C2×#10625122 | C2 | semidirect |
| 5. C2×#10625115 | C2 | semidirect |
| 6. #13092810 | C2 | semidirect |
| 7. #13092808 | C2 | semidirect |
| 8. #13092795 | C2 | semidirect |
| 9. #13092788 | C2 | semidirect |
| 10. M16×Dic23 | C2 | semidirect |
| 11. C2×C23×#137 | C2 | semidirect |
| 70. M16×C23 | D4 | semidirect |
| 84. #67267 | D4 | semidirect |
| 141. Dic23 | #137 | semidirect |
| 145. C2×#137 | D23 | semidirect |
| 189. C23 | #3152 | semidirect |
| 224. M16 | C22⋊D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625080 | 2 |
| C2×#10625113 | 2 |
| C2×#10625122 | 2 |
| #13092963 | 2 |
| C2×#10625115 | 2 |
| #13092810 | 2 |
| #13092808 | 2 |
| #13092795 | 2 |
| #13092788 | 2 |
| M16×Dic23 | 2 |
| C2×C23×#137 | 2 |
| #3152 | 23 |