Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
230 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 230 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. #20260761 | C2 | semidirect |
| 5. #20260500 | C2 | semidirect |
| 6. #20260495 | C2 | semidirect |
| 7. C2×C4×C8×C97 | C2 | semidirect |
| 14. #15690735 | C4 | semidirect |
| 15. #15690732 | C4 | semidirect |
| 91. C97 | #1937 | semidirect |
| 96. C2×C4×C8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260761 | 2 |
| C2×#15690738 | 2 |
| #20260732 | 2 |
| #20260701 | 2 |
| #20260500 | 2 |
| #20260495 | 2 |
| C2×C4×C8×C97 | 2 |
| #1937 | 97 |