Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
296 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #20260502 | C2 | semidirect |
| 5. #20260501 | C2 | semidirect |
| 6. #20260501 | C2 | semidirect |
| 7. #342×C97 | C2 | semidirect |
| 11. #15690766 | C4 | semidirect |
| 15. C22⋊C4×D97 | C4 | semidirect |
| 119. C97 | #1828 | semidirect |
| 126. #342 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261208 | 2 |
| C2×#15690724 | 2 |
| #20260502 | 2 |
| #20260501 | 2 |
| #342×C97 | 2 |
| #1828 | 97 |