Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
598 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 105 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. C22×C22⋊Dic97 | C2 | semidirect |
| 2. C2×#15690725 | C2 | semidirect |
| 3. #20260591 | C2 | semidirect |
| 4. #20260502 | C2 | semidirect |
| 14. C22×D4×C97 | C4 | semidirect |
| 19. C2×C22⋊C4×C97 | C4 | semidirect |
| 30. C22⋊Dic97 | D4 | semidirect |
| 35. C24×C97 | C2×C4 | semidirect |
| 47. C22×C4×C97 | C2×C4 | semidirect |
| 48. C22×C4×C97 | C2×C4 | semidirect |
| 111. C22×C97 | #99 | semidirect |
| 131. C97 | #1898 | semidirect |
| 138. C22×D4 | Dic97 | semidirect |
| 149. C2×C22⋊C4 | Dic97 | semidirect |
| 156. C24 | C2×Dic97 | semidirect |
| 172. C22×C4 | C2×Dic97 | semidirect |
| 173. C22×C4 | C2×Dic97 | semidirect |
| 242. C22 | #15690725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic97 | 2 |
| C2×#15690725 | 2 |
| #20260591 | 2 |
| #20260502 | 2 |
| C2×#120×C97 | 2 |
| #1898 | 97 |