Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×Q8×Dic97 | C2 | semidirect |
| 4. #20260959 | C2 | semidirect |
| 5. #20260955 | C2 | semidirect |
| 6. #20260943 | C2 | semidirect |
| 7. #20260933 | C2 | semidirect |
| 8. #20260758 | C2 | semidirect |
| 9. #20260737 | C2 | semidirect |
| 10. #20260736 | C2 | semidirect |
| 11. C2×#137×C97 | C2 | semidirect |
| 80. C2×Q8×C97 | D4 | semidirect |
| 150. Dic97 | #137 | semidirect |
| 158. C97 | #3037 | semidirect |
| 160. C2×#137 | D97 | semidirect |
| 210. 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 |
| #20261281 | 2 |
| C2×Q8×Dic97 | 2 |
| #20260959 | 2 |
| #20260955 | 2 |
| #20260943 | 2 |
| #20260933 | 2 |
| #20260758 | 2 |
| #20260737 | 2 |
| #20260736 | 2 |
| C2×#137×C97 | 2 |
| #3037 | 97 |