Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20260808 | C2 | semidirect |
| 4. #20260759 | C2 | semidirect |
| 5. #20260701 | C2 | semidirect |
| 6. C2×#97×C97 | C2 | semidirect |
| 39. C2×C8×C97 | D4 | semidirect |
| 80. C97 | #2932 | semidirect |
| 86. C2×#97 | D97 | semidirect |
| 117. C2×C8 | D388 | 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 |
| #20260808 | 2 |
| #20260759 | 2 |
| #20260701 | 2 |
| C2×#97×C97 | 2 |
| #2932 | 97 |