Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20260990 | C2 | semidirect |
| 4. #20260973 | C2 | semidirect |
| 5. #20260773 | C2 | semidirect |
| 6. #20260744 | C2 | semidirect |
| 7. C22×Q16×C97 | C2 | semidirect |
| 89. C97 | #3059 | semidirect |
| 90. C22×Q16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690816 | 2 |
| #20261309 | 2 |
| #20260990 | 2 |
| #20260973 | 2 |
| #20260773 | 2 |
| #20260744 | 2 |
| C22×Q16×C97 | 2 |
| #3059 | 97 |