Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #20261101 | C2 | semidirect |
| 3. #20261097 | C2 | semidirect |
| 4. #20261092 | C2 | semidirect |
| 5. #20261083 | C2 | semidirect |
| 6. #20260739 | C2 | semidirect |
| 7. #20260734 | C2 | semidirect |
| 8. #20260729 | C2 | semidirect |
| 9. C2×#15690730 | C2 | semidirect |
| 10. #20260691 | C2 | semidirect |
| 11. #544×C97 | C2 | semidirect |
| 21. #15690733 | C22 | semidirect |
| 22. #15690733 | C22 | semidirect |
| 23. #15690733 | C22 | semidirect |
| 28. #15690730 | C22 | semidirect |
| 29. #15690730 | C22 | semidirect |
| 30. #15690730 | C22 | semidirect |
| 31. #15690721 | C22 | semidirect |
| 32. C4×#11715895 | C22 | semidirect |
| 34. C4⋊Q8×C97 | C22 | semidirect |
| 36. #125×C97 | C22 | semidirect |
| 136. C97 | #3136 | semidirect |
| 137. #544 | D97 | semidirect |
| 153. C4⋊Q8 | C2×D97 | semidirect |
| 156. #125 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261304 | 2 |
| #20261101 | 2 |
| #20261097 | 2 |
| #20261092 | 2 |
| #20261083 | 2 |
| #20260739 | 2 |
| #20260734 | 2 |
| #20260729 | 2 |
| C2×#15690730 | 2 |
| #20260691 | 2 |
| #544×C97 | 2 |
| #3136 | 97 |