Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 2. #20261313 | C2 | semidirect |
| 3. #20260978 | C2 | semidirect |
| 4. #20260973 | C2 | semidirect |
| 5. #20260968 | C2 | semidirect |
| 6. C2×#15690744 | C2 | semidirect |
| 7. #20260736 | C2 | semidirect |
| 8. C2×#135×C97 | C2 | semidirect |
| 57. C2×C8×C97 | D4 | semidirect |
| 109. C97 | #3061 | semidirect |
| 110. C2×#135 | D97 | semidirect |
| 161. C2×C8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690816 | 2 |
| #20261313 | 2 |
| #20260978 | 2 |
| #20260973 | 2 |
| #20260968 | 2 |
| C2×#15690744 | 2 |
| #20260736 | 2 |
| C2×#135×C97 | 2 |
| #3061 | 97 |