Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26040009 | C2 | semidirect |
| 2. #26040007 | C2 | semidirect |
| 3. #26040003 | C2 | semidirect |
| 4. #26039998 | C2 | semidirect |
| 5. #26039994 | C2 | semidirect |
| 7. C4×Dic718 | C2 | semidirect |
| 8. C4×D1436 | C2 | semidirect |
| 9. C4×C22⋊D359 | C2 | semidirect |
| 10. #26039972 | C2 | semidirect |
| 11. C2×C42×C359 | C2 | semidirect |
| 74. C359 | #529 | semidirect |
| 86. C2×C42 | D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040009 | 2 |
| #26040007 | 2 |
| #26040003 | 2 |
| #26039998 | 2 |
| #26039994 | 2 |
| #26039989 | 2 |
| C4×Dic718 | 2 |
| C4×D1436 | 2 |
| C4×C22⋊D359 | 2 |
| #26039972 | 2 |
| C2×C42×C359 | 2 |
| #529 | 359 |