Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #20260743 | C2 | semidirect |
| 5. #20260641 | C2 | semidirect |
| 6. #20260503 | C2 | semidirect |
| 7. #339×C97 | C2 | semidirect |
| 11. #15690843 | C4 | semidirect |
| 37. C2×Dic194 | C2×C4 | semidirect |
| 58. M16×C97 | C2×C4 | semidirect |
| 125. C97 | #1882 | semidirect |
| 132. #339 | D97 | semidirect |
| 177. M16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690843 | 2 |
| #20261215 | 2 |
| C2×#15690738 | 2 |
| #20260743 | 2 |
| #20260641 | 2 |
| #20260503 | 2 |
| #339×C97 | 2 |
| #1882 | 97 |