Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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×C42×D97 | C2 | semidirect |
| 2. #20260623 | C2 | semidirect |
| 3. #20260616 | C2 | semidirect |
| 5. #20260606 | C2 | semidirect |
| 6. #20260603 | C2 | semidirect |
| 7. C2×#126×C97 | C2 | semidirect |
| 40. C42×C97 | D4 | semidirect |
| 71. C2×D97 | #126 | semidirect |
| 83. C97 | #2852 | semidirect |
| 84. C2×#126 | D97 | semidirect |
| 123. C42 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D97 | 2 |
| #20260623 | 2 |
| #20260616 | 2 |
| #20260611 | 2 |
| #20260606 | 2 |
| #20260603 | 2 |
| C2×#126×C97 | 2 |
| #2852 | 97 |