Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
504 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 1. #20260634 | C2 | semidirect |
| 3. #20260601 | C2 | semidirect |
| 5. C4⋊C4×Dic97 | C2 | semidirect |
| 7. #20260581 | C2 | semidirect |
| 21. #117×C97 | C4 | semidirect |
| 95. C97 | #2346 | semidirect |
| 105. #117 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260634 | 2 |
| #20260628 | 2 |
| #20260601 | 2 |
| #20260595 | 2 |
| C4⋊C4×Dic97 | 2 |
| C4×C22⋊Dic97 | 2 |
| #20260581 | 2 |
| C2×#117×C97 | 2 |
| #2346 | 97 |