Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
356 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 145 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. #20261138 | C2 | semidirect |
| 3. #20261135 | C2 | semidirect |
| 4. #20261133 | C2 | semidirect |
| 7. #498×C97 | C2 | semidirect |
| 28. C8×D97 | Q8 | semidirect |
| 68. C97 | #3160 | semidirect |
| 73. #498 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| #20261138 | 2 |
| #20261135 | 2 |
| #20261133 | 2 |
| #20260770 | 2 |
| C4×C8×D97 | 2 |
| #498×C97 | 2 |
| #3160 | 97 |