Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
440 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 209 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 |
|---|---|---|
| 3. #20260784 | C2 | semidirect |
| 4. #20260782 | C2 | semidirect |
| 5. C2×#15690745 | C2 | semidirect |
| 6. #108×D97 | C2 | semidirect |
| 7. #430×C97 | C2 | semidirect |
| 76. C97 | #2916 | semidirect |
| 81. #430 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261501 | 2 |
| C2×#15690818 | 2 |
| #20260784 | 2 |
| #20260782 | 2 |
| C2×#15690745 | 2 |
| #108×D97 | 2 |
| #430×C97 | 2 |
| #2916 | 97 |