Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
480 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. C2×#15690745 | C2 | direct (N × H) |
| 11. #15690745 | C22 | direct (N × H) |
| 50. C22×C97 | #108 | semidirect |
| 60. C2×C97 | C2×#108 | semidirect |
| 63. C97 | C22×#108 | semidirect |
| 113. C22 | #15690745 | direct (N × H) |
| 123. C2 | C2×#15690745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095495 | 2 |
| C23×#11715895 | 2 |
| C2×#15690745 | 2 |
| C22×M16×C97 | 2 |
| C22×#108 | 97 |