Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 11. #15690775 | C4 | semidirect |
| 83. Dic194 | C4⋊C4 | semidirect |
| 102. Dic97 | #103 | semidirect |
| 111. C97 | #1803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690775 | 2 |
| C2×#15690739 | 2 |
| C2×#15690735 | 2 |
| C2×#15690733 | 2 |
| #20260604 | 2 |
| #20260497 | 2 |
| #340×C97 | 2 |
| #1803 | 97 |