Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20261032 | C2 | semidirect |
| 3. #20261032 | C2 | semidirect |
| 4. #20261022 | C2 | semidirect |
| 5. #20261012 | C2 | semidirect |
| 6. #20260775 | C2 | semidirect |
| 7. #20260771 | C2 | semidirect |
| 8. #20260762 | C2 | semidirect |
| 11. #544×C97 | C2 | semidirect |
| 21. #15690743 | C22 | semidirect |
| 22. #15690743 | C22 | semidirect |
| 23. #15690743 | C22 | semidirect |
| 24. #15690741 | C22 | semidirect |
| 25. #15690741 | C22 | semidirect |
| 26. #15690741 | C22 | semidirect |
| 27. C4⋊#11715895 | C22 | semidirect |
| 28. C4⋊#11715895 | C22 | semidirect |
| 34. C4⋊Q8×C97 | C22 | semidirect |
| 36. #125×C97 | C22 | semidirect |
| 44. C2×D388 | Q8 | semidirect |
| 125. C97 | #3081 | semidirect |
| 126. #544 | D97 | semidirect |
| 141. C4⋊Q8 | C2×D97 | semidirect |
| 143. #125 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261209 | 2 |
| #20261032 | 2 |
| #20261022 | 2 |
| #20261012 | 2 |
| #20260775 | 2 |
| #20260771 | 2 |
| #20260762 | 2 |
| #20260739 | 2 |
| C2×#15690730 | 2 |
| #544×C97 | 2 |
| #3081 | 97 |