Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
250 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 65 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. #20260719 | C2 | semidirect |
| 3. #20260533 | C2 | semidirect |
| 4. #20260531 | C2 | semidirect |
| 5. #413×C97 | C2 | semidirect |
| 112. C97 | #2132 | semidirect |
| 115. #413 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261281 | 2 |
| #20260719 | 2 |
| #20260533 | 2 |
| #20260531 | 2 |
| #413×C97 | 2 |
| #2132 | 97 |