Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
260 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 77 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×#15690729 | C2 | semidirect |
| 2. #20260532 | C2 | direct (N × H) |
| 6. #15690729 | C22 | semidirect |
| 71. C2×C97 | #355 | semidirect |
| 74. C97 | C2×#355 | semidirect |
| 145. C2 | #20260532 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690729 | 2 |
| #20260532 | 2 |
| C2×#124×C97 | 2 |
| C2×#355 | 97 |