Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×Q16×D23 | C2 | semidirect |
| 3. #13092795 | C2 | semidirect |
| 4. #13092658 | C2 | semidirect |
| 5. #13092655 | C2 | semidirect |
| 6. #13092625 | C2 | semidirect |
| 7. #13092573 | C2 | semidirect |
| 8. #13092571 | C2 | semidirect |
| 9. Q16×Dic23 | C2 | semidirect |
| 11. C22×Q16×C23 | C2 | semidirect |
| 57. Q16×C23 | D4 | semidirect |
| 94. C22⋊D23 | Q16 | direct (N × H) |
| 113. C22×C23 | C2×Q16 | semidirect |
| 117. C2×D23 | C2×Q16 | semidirect |
| 127. Dic23 | C2×Q16 | semidirect |
| 129. C22×Q16 | D23 | semidirect |
| 173. C23 | D4×Q16 | semidirect |
| 193. Q16 | C22⋊D23 | direct (N × H) |
| 248. C22 | Q16×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D23 | 2 |
| Q8×C22⋊D23 | 2 |
| #13092795 | 2 |
| #13092658 | 2 |
| #13092655 | 2 |
| #13092625 | 2 |
| #13092573 | 2 |
| #13092571 | 2 |
| Q16×Dic23 | 2 |
| C8×C22⋊D23 | 2 |
| C22×Q16×C23 | 2 |
| D4×Q16 | 23 |