Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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. #13092900 | C2 | semidirect |
| 2. C2×#10625019 | C2 | semidirect |
| 3. #13092422 | C2 | semidirect |
| 4. #13092320 | C2 | semidirect |
| 5. #13092185 | C2 | semidirect |
| 6. #13092178 | C2 | semidirect |
| 11. C23×AGL(1,ℤ/8) | C4 | semidirect |
| 40. C2×D4×C23 | C2×C4 | semidirect |
| 50. M16×C23 | C2×C4 | semidirect |
| 75. Q8×C23 | C22⋊C4 | semidirect |
| 83. D4×C23 | C22⋊C4 | semidirect |
| 143. AGL(1,ℤ/8) | Dic23 | semidirect |
| 160. C23 | #1883 | semidirect |
| 173. C2×D4 | C2×Dic23 | semidirect |
| 185. M16 | C2×Dic23 | semidirect |
| 208. Q8 | C22⋊Dic23 | semidirect |
| 216. D4 | C22⋊Dic23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092900 | 2 |
| C2×#10625019 | 2 |
| #13092422 | 2 |
| #13092320 | 2 |
| #13092185 | 2 |
| #13092178 | 2 |
| C2×C23×AGL(1,ℤ/8) | 2 |
| #1883 | 23 |