Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 9. #15690809 | C4 | semidirect |
| 10. #15690801 | C4 | semidirect |
| 38. C4×Dic97 | Q8 | semidirect |
| 48. C42×C97 | Q8 | semidirect |
| 87. C97 | #1994 | semidirect |
| 135. C42 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261288 | 2 |
| #20260758 | 2 |
| C42×Dic97 | 2 |
| #20260496 | 2 |
| #20260495 | 2 |
| #20260494 | 2 |
| #339×C97 | 2 |
| #1994 | 97 |