Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 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 |
|---|---|---|
| 1. C2×#15690841 | C2 | semidirect |
| 3. #20261213 | C2 | semidirect |
| 4. #20260955 | C2 | semidirect |
| 5. #20260933 | C2 | semidirect |
| 6. #20260761 | C2 | semidirect |
| 7. #20260740 | C2 | semidirect |
| 8. #20260732 | C2 | semidirect |
| 9. C22×SD16×C97 | C2 | semidirect |
| 12. C2×#13095501 | C22 | semidirect |
| 13. C2×#13095498 | C22 | semidirect |
| 20. Q8×Dic97 | C22 | semidirect |
| 24. #15690739 | C22 | semidirect |
| 25. #15690735 | C22 | semidirect |
| 26. #15690732 | C22 | semidirect |
| 56. C2×Q8×C97 | D4 | semidirect |
| 117. C97 | #3043 | semidirect |
| 119. C22×SD16 | D97 | semidirect |
| 156. C2×Q8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690841 | 2 |
| #20261302 | 2 |
| #20261213 | 2 |
| #20260955 | 2 |
| #20260933 | 2 |
| #20260761 | 2 |
| #20260740 | 2 |
| #20260732 | 2 |
| C22×SD16×C97 | 2 |
| #3043 | 97 |