Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
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. #20263320 | C2 | semidirect |
| 2. #20263318 | C2 | semidirect |
| 3. #20263314 | C2 | semidirect |
| 4. #20263309 | C2 | semidirect |
| 5. #20263305 | C2 | semidirect |
| 7. C4×Dic394 | C2 | semidirect |
| 8. C4×D788 | C2 | semidirect |
| 9. C4×C22⋊D197 | C2 | semidirect |
| 10. #20263283 | C2 | semidirect |
| 11. C2×C42×C197 | C2 | semidirect |
| 74. C197 | #529 | semidirect |
| 86. C2×C42 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263320 | 2 |
| #20263318 | 2 |
| #20263314 | 2 |
| #20263309 | 2 |
| #20263305 | 2 |
| #20263300 | 2 |
| C4×Dic394 | 2 |
| C4×D788 | 2 |
| C4×C22⋊D197 | 2 |
| #20263283 | 2 |
| C2×C42×C197 | 2 |
| #529 | 197 |