Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
260 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 117 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×#15690750 | C2 | semidirect |
| 2. C22⋊#13095486 | C2 | semidirect |
| 5. C2×#13095486 | C22 | semidirect |
| 48. C22×C97 | M32 | semidirect |
| 59. C97 | #2112 | semidirect |
| 107. C22 | #15690750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690750 | 2 |
| C22⋊#13095486 | 2 |
| C23×C8×C97 | 2 |
| #2112 | 97 |