Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
240 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 13. #15690743 | C4 | semidirect |
| 73. #11715895 | C4⋊C4 | semidirect |
| 99. C97 | #1943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690743 | 2 |
| C2×#15690741 | 2 |
| C2×#15690721 | 2 |
| #20260633 | 2 |
| #20260497 | 2 |
| #389×C97 | 2 |
| #1943 | 97 |