Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. C2×#15690880 | C2 | semidirect |
| 4. #20261611 | C2 | semidirect |
| 68. C22×C97 | #108 | semidirect |
| 89. C97 | #1855 | semidirect |
| 164. C22 | #15690880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095521 | 2 |
| C2×#15690880 | 2 |
| #20261706 | 2 |
| #20261611 | 2 |
| C22⋊C8×D97 | 2 |
| #1855 | 97 |