Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20263324 | C2 | semidirect |
| 2. #20263316 | C2 | semidirect |
| 3. #20263316 | C2 | semidirect |
| 4. #20263304 | C2 | semidirect |
| 5. #20263304 | C2 | semidirect |
| 6. #20263303 | C2 | semidirect |
| 7. #20263303 | C2 | semidirect |
| 8. #20263302 | C2 | semidirect |
| 9. #20263291 | C2 | semidirect |
| 13. C2×#15691337 | C2 | semidirect |
| 14. C4⋊C4×D197 | C2 | semidirect |
| 15. C22⋊Q8×C197 | C2 | semidirect |
| 54. C22⋊D197 | Q8 | semidirect |
| 101. C197 | #554 | semidirect |
| 111. C22⋊Q8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263324 | 2 |
| #20263316 | 2 |
| #20263304 | 2 |
| #20263303 | 2 |
| #20263302 | 2 |
| #20263291 | 2 |
| C4×C22⋊D197 | 2 |
| #20263286 | 2 |
| C2×#15691337 | 2 |
| C4⋊C4×D197 | 2 |
| C22⋊Q8×C197 | 2 |
| #554 | 197 |