Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
552 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 552 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. #13092797 | C2 | semidirect |
| 4. #13092796 | C2 | semidirect |
| 5. #13092795 | C2 | semidirect |
| 7. C23×#494 | C2 | semidirect |
| 51. C4×D23 | Q16 | semidirect |
| 62. C4×C23 | C2×Q16 | semidirect |
| 66. Dic23 | C2×Q16 | semidirect |
| 72. #494 | D23 | direct (N × H) |
| 76. D23 | #494 | direct (N × H) |
| 92. C23 | C2×#494 | semidirect |
| 134. C4 | 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 |
| C4⋊Q8×D23 | 2 |
| #13092797 | 2 |
| #13092796 | 2 |
| #13092795 | 2 |
| C4×C8×D23 | 2 |
| C23×#494 | 2 |
| C2×#494 | 23 |