Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20260778 | C2 | semidirect |
| 5. #20260503 | C2 | semidirect |
| 6. #20260500 | C2 | semidirect |
| 7. #405×C97 | C2 | semidirect |
| 18. #15690726 | C4 | semidirect |
| 101. C97 | #1931 | semidirect |
| 106. #405 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260778 | 2 |
| #20260739 | 2 |
| C2×#15690732 | 2 |
| C2×#15690726 | 2 |
| #20260503 | 2 |
| #20260500 | 2 |
| #405×C97 | 2 |
| #1931 | 97 |