Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. C2×#15690730 | C2 | semidirect |
| 3. C2×#15690720 | C2 | semidirect |
| 4. #20260636 | C2 | semidirect |
| 5. C2×#106×C97 | C2 | semidirect |
| 9. C2×D776 | C4 | semidirect |
| 60. C8×C97 | C22⋊C4 | semidirect |
| 83. C97 | #1972 | semidirect |
| 85. C2×#106 | D97 | semidirect |
| 144. C8 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C2×#15690730 | 2 |
| C2×#15690720 | 2 |
| #20260636 | 2 |
| C2×#106×C97 | 2 |
| #1972 | 97 |