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. #20261140 | C2 | semidirect |
| 3. #20261136 | C2 | semidirect |
| 4. #20261131 | C2 | semidirect |
| 7. #500×C97 | C2 | semidirect |
| 29. C8×D97 | Q8 | semidirect |
| 77. C97 | #3160 | semidirect |
| 80. #500 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| #20261140 | 2 |
| #20261136 | 2 |
| #20261131 | 2 |
| #20260772 | 2 |
| C4×C8×D97 | 2 |
| #500×C97 | 2 |
| #3160 | 97 |