Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
148 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 10. #15690756 | C4 | semidirect |
| 64. C97 | #2176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690756 | 2 |
| C4×Dic388 | 2 |
| #20260562 | 2 |
| #20260539 | 2 |
| #20260538 | 2 |
| #20260511 | 2 |
| C4×Q16×C97 | 2 |
| #2176 | 97 |