Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
880 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#15690725 | C2 | semidirect |
| 2. #20260591 | C2 | semidirect |
| 5. C2×C22⋊Dic97 | C22 | semidirect |
| 7. C25×C97 | C4 | semidirect |
| 11. C22×D4×C97 | C4 | semidirect |
| 13. C23×C4×C97 | C4 | semidirect |
| 55. C23×C97 | C22⋊C4 | semidirect |
| 64. C2×C4×C97 | C22⋊C4 | semidirect |
| 82. C22×C97 | #99 | semidirect |
| 96. C97 | #1781 | semidirect |
| 100. C25 | Dic97 | semidirect |
| 104. C22×D4 | Dic97 | semidirect |
| 106. C23×C4 | Dic97 | semidirect |
| 151. C23 | C22⋊Dic97 | semidirect |
| 162. C2×C4 | C22⋊Dic97 | semidirect |
| 178. C22 | #15690725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690725 | 2 |
| #20260591 | 2 |
| C23×D4×C97 | 2 |
| #1781 | 97 |