Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 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. #20263325 | C2 | semidirect |
| 2. #20263321 | C2 | semidirect |
| 3. #20263315 | C2 | semidirect |
| 4. #20263312 | C2 | semidirect |
| 5. #20263308 | C2 | semidirect |
| 6. #20263306 | C2 | semidirect |
| 8. Q8×Dic197 | C2 | semidirect |
| 9. #20263288 | C2 | semidirect |
| 10. #20263285 | C2 | semidirect |
| 11. C22⋊Q8×C197 | C2 | semidirect |
| 73. C197 | #542 | semidirect |
| 81. C22⋊Q8 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263325 | 2 |
| #20263321 | 2 |
| #20263315 | 2 |
| #20263312 | 2 |
| #20263308 | 2 |
| #20263306 | 2 |
| #20263300 | 2 |
| Q8×Dic197 | 2 |
| #20263288 | 2 |
| #20263285 | 2 |
| C22⋊Q8×C197 | 2 |
| #542 | 197 |