Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 190 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 |
|---|---|---|
| 1. #20261131 | C2 | semidirect |
| 3. #20261087 | C2 | semidirect |
| 6. C8×#11715895 | C2 | semidirect |
| 7. #487×C97 | C2 | semidirect |
| 69. C97 | #1708 | semidirect |
| 73. #487 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261131 | 2 |
| #20261109 | 2 |
| #20261087 | 2 |
| #20261083 | 2 |
| #20261082 | 2 |
| C8×#11715895 | 2 |
| #487×C97 | 2 |
| #1708 | 97 |