Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20263321 | C2 | semidirect |
| 3. #20263319 | C2 | semidirect |
| 4. #20263315 | C2 | semidirect |
| 5. #20263312 | C2 | semidirect |
| 6. #20263312 | C2 | semidirect |
| 7. #20263311 | C2 | semidirect |
| 8. #20263309 | C2 | semidirect |
| 9. #20263304 | C2 | semidirect |
| 10. #20263304 | C2 | semidirect |
| 12. #20263291 | C2 | semidirect |
| 13. C4×C22⋊D197 | C2 | semidirect |
| 14. #20263284 | C2 | semidirect |
| 15. C22⋊Q8×C197 | C2 | semidirect |
| 103. C197 | #542 | semidirect |
| 115. 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 |
| #20263321 | 2 |
| #20263319 | 2 |
| #20263315 | 2 |
| #20263312 | 2 |
| #20263311 | 2 |
| #20263309 | 2 |
| #20263304 | 2 |
| #20263299 | 2 |
| #20263291 | 2 |
| C4×C22⋊D197 | 2 |
| #20263284 | 2 |
| C22⋊Q8×C197 | 2 |
| #542 | 197 |