Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
780 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 325 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 |
|---|---|---|
| 2. #13092268 | C2 | semidirect |
| 3. C4×C22⋊Dic23 | C2 | semidirect |
| 4. #13092264 | C2 | semidirect |
| 5. #13092262 | C2 | semidirect |
| 6. #95×D23 | C2 | semidirect |
| 7. C2×C23×#95 | C2 | semidirect |
| 12. C4×C22⋊D23 | C4 | semidirect |
| 24. C22×C4×C23 | C2×C4 | semidirect |
| 32. C2×C4×D23 | C2×C4 | semidirect |
| 33. C22⋊Dic23 | C2×C4 | semidirect |
| 34. (C2×D23)⋊C4 | C2×C4 | semidirect |
| 35. Dic23⋊C4 | C2×C4 | semidirect |
| 37. C4×Dic23 | C2×C4 | semidirect |
| 50. C22⋊D23 | C42 | semidirect |
| 79. C2×#95 | D23 | semidirect |
| 98. C23 | #2275 | semidirect |
| 108. C22×C4 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D23 | 2 |
| #13092268 | 2 |
| C4×C22⋊Dic23 | 2 |
| #13092264 | 2 |
| #13092262 | 2 |
| #95×D23 | 2 |
| C2×C23×#95 | 2 |
| #2275 | 23 |