Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20261022 | C2 | semidirect |
| 4. #20261012 | C2 | semidirect |
| 5. #20260778 | C2 | semidirect |
| 6. #20260759 | C2 | semidirect |
| 8. #533×C97 | C2 | semidirect |
| 18. #15690743 | C22 | semidirect |
| 19. #15690741 | C22 | semidirect |
| 20. C4⋊#11715895 | C22 | semidirect |
| 21. C4⋊#11715895 | C22 | semidirect |
| 24. C4⋊Q8×C97 | C22 | semidirect |
| 25. C4⋊Q8×C97 | C22 | semidirect |
| 26. #125×C97 | C22 | semidirect |
| 36. C2×D388 | Q8 | semidirect |
| 116. C97 | #3077 | semidirect |
| 117. #533 | D97 | semidirect |
| 128. C4⋊Q8 | C2×D97 | semidirect |
| 129. C4⋊Q8 | C2×D97 | semidirect |
| 130. #125 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| #20261032 | 2 |
| #20261022 | 2 |
| #20261012 | 2 |
| #20260778 | 2 |
| #20260759 | 2 |
| #20260739 | 2 |
| #533×C97 | 2 |
| #3077 | 97 |