Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
582 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15690804 | C2 | semidirect |
| 2. #20260626 | C2 | semidirect |
| 3. #20260619 | C2 | semidirect |
| 5. #20260608 | C2 | semidirect |
| 6. #20260603 | C2 | semidirect |
| 7. C22×C42×C97 | C2 | semidirect |
| 40. C42×C97 | D4 | semidirect |
| 65. C22×C97 | #126 | semidirect |
| 83. C97 | #2852 | semidirect |
| 85. C22×C42 | D97 | semidirect |
| 123. C42 | C22⋊D97 | semidirect |
| 151. C22 | #15690804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690804 | 2 |
| #20260626 | 2 |
| #20260619 | 2 |
| #20260614 | 2 |
| #20260608 | 2 |
| #20260603 | 2 |
| C22×C42×C97 | 2 |
| #2852 | 97 |