Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 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. #20261552 | C2 | semidirect |
| 2. #20261176 | C2 | semidirect |
| 3. #20261175 | C2 | semidirect |
| 4. #20261165 | C2 | semidirect |
| 5. C2×#15690756 | C2 | semidirect |
| 6. #20261152 | C2 | semidirect |
| 7. #578×C97 | C2 | semidirect |
| 74. C97 | #3417 | semidirect |
| 76. #578 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261552 | 2 |
| #20261176 | 2 |
| #20261175 | 2 |
| #20261165 | 2 |
| C2×#15690756 | 2 |
| #20261152 | 2 |
| #578×C97 | 2 |
| #3417 | 97 |