Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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. #20261292 | C2 | semidirect |
| 2. #20261035 | C2 | semidirect |
| 3. #20261025 | C2 | semidirect |
| 4. #20261015 | C2 | semidirect |
| 5. #20260775 | C2 | semidirect |
| 6. #20260759 | C2 | semidirect |
| 10. #15690810 | C22 | semidirect |
| 11. #15690810 | C22 | semidirect |
| 12. #15690802 | C22 | semidirect |
| 18. #15690743 | C22 | semidirect |
| 19. #15690741 | C22 | semidirect |
| 20. C4⋊#11715895 | C22 | semidirect |
| 21. C4⋊#11715895 | C22 | semidirect |
| 48. C2×D4×C97 | Q8 | semidirect |
| 116. C97 | #3077 | semidirect |
| 154. C2×D4 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261292 | 2 |
| #20261035 | 2 |
| #20261025 | 2 |
| #20261015 | 2 |
| #20260775 | 2 |
| #20260759 | 2 |
| #20260740 | 2 |
| C2×C4×D4×C97 | 2 |
| #3077 | 97 |