Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
736 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 736 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×#15690728 | C2 | direct (N × H) |
| 15. #15690728 | C22 | direct (N × H) |
| 69. C22×C97 | #101 | semidirect |
| 80. C2×C97 | C2×#101 | semidirect |
| 83. C97 | C22×#101 | semidirect |
| 152. C22 | #15690728 | direct (N × H) |
| 163. C2 | C2×#15690728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic194 | 2 |
| C22×#13095495 | 2 |
| C2×#15690728 | 2 |
| C22×M16×C97 | 2 |
| C22×#101 | 97 |