Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
126 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 32 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. #20261630 | C2 | semidirect |
| 2. #20261609 | C2 | semidirect |
| 8. #15690744 | C4 | semidirect |
| 10. C2×D8×C97 | C4 | semidirect |
| 60. C97 | #1347 | semidirect |
| 64. C2×D8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261630 | 2 |
| #20261609 | 2 |
| #20260968 | 2 |
| #1347 | 97 |