Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#15690816 | C2 | semidirect |
| 3. #20260814 | C2 | semidirect |
| 4. C8×D388 | C2 | semidirect |
| 5. #20260759 | C2 | semidirect |
| 6. #20260701 | C2 | semidirect |
| 7. C2×C4×C8×C97 | C2 | semidirect |
| 41. C2×C8×C97 | D4 | semidirect |
| 75. C4×C97 | #131 | semidirect |
| 84. C97 | #2931 | semidirect |
| 91. C2×C4×C8 | D97 | semidirect |
| 123. C2×C8 | D388 | semidirect |
| 160. C4 | #15690816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690816 | 2 |
| #20261285 | 2 |
| #20260814 | 2 |
| C8×D388 | 2 |
| #20260759 | 2 |
| #20260701 | 2 |
| C2×C4×C8×C97 | 2 |
| #2931 | 97 |