Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20261082 | C2 | semidirect |
| 3. #20261015 | C2 | semidirect |
| 4. #20260946 | C2 | semidirect |
| 5. #20260478 | C2 | semidirect |
| 6. #20260467 | C2 | semidirect |
| 7. D4⋊C8×C97 | C2 | semidirect |
| 100. C97 | #1641 | semidirect |
| 107. D4⋊C8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261406 | 2 |
| #20261082 | 2 |
| #20261015 | 2 |
| #20260946 | 2 |
| #20260478 | 2 |
| #20260467 | 2 |
| D4⋊C8×C97 | 2 |
| #1641 | 97 |