Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 3. #13092655 | C2 | direct (N × H) |
| 4. C2×#10625000 | C2 | semidirect |
| 5. C2×#10625017 | C2 | semidirect |
| 6. C22×Q16×C23 | C2 | semidirect |
| 10. C2×Q16×C23 | C22 | semidirect |
| 20. #10625017 | C22 | semidirect |
| 21. #10625000 | C22 | semidirect |
| 48. C22×D23 | Q16 | semidirect |
| 76. C2×D23 | C2×Q16 | semidirect |
| 83. C22×Q16 | D23 | semidirect |
| 89. C2×C23 | #467 | semidirect |
| 97. C2×Q16 | C2×D23 | semidirect |
| 109. C23 | C2×#467 | semidirect |
| 171. C2 | #13092655 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D23 | 2 |
| C2×#10625117 | 2 |
| #13092655 | 2 |
| C2×#10625000 | 2 |
| C2×#10625017 | 2 |
| C22×Q16×C23 | 2 |
| C2×#467 | 23 |