Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26040010 | C2 | semidirect |
| 2. #26040005 | C2 | semidirect |
| 3. #26040000 | C2 | semidirect |
| 4. #26039998 | C2 | semidirect |
| 5. #26039994 | C2 | semidirect |
| 6. #26039993 | C2 | semidirect |
| 8. C4×C22⋊D359 | C2 | semidirect |
| 9. C2×C4⋊C4×C359 | C2 | semidirect |
| 66. C359 | #539 | semidirect |
| 76. C2×C4⋊C4 | D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040010 | 2 |
| #26040005 | 2 |
| #26040000 | 2 |
| #26039998 | 2 |
| #26039994 | 2 |
| #26039993 | 2 |
| #26039989 | 2 |
| C4×C22⋊D359 | 2 |
| C2×C4⋊C4×C359 | 2 |
| #539 | 359 |