Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 302 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 |
|---|---|---|
| 2. #20260778 | C2 | semidirect |
| 5. #20260605 | C2 | semidirect |
| 6. #20260503 | C2 | semidirect |
| 7. #339×C97 | C2 | semidirect |
| 20. #15690738 | C4 | semidirect |
| 38. #13095495 | C2×C4 | semidirect |
| 58. C42×C97 | C2×C4 | semidirect |
| 80. D388 | C4⋊C4 | semidirect |
| 85. Dic194 | C4⋊C4 | semidirect |
| 113. C97 | #1859 | semidirect |
| 120. #339 | D97 | semidirect |
| 171. C42 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261215 | 2 |
| #20260778 | 2 |
| C2×#15690738 | 2 |
| #20260737 | 2 |
| #20260605 | 2 |
| #20260503 | 2 |
| #339×C97 | 2 |
| #1859 | 97 |