Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 262 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. #20260495 | C2 | semidirect |
| 5. #20260492 | C2 | semidirect |
| 6. #20260491 | C2 | semidirect |
| 7. #339×C97 | C2 | semidirect |
| 15. #15690767 | C4 | semidirect |
| 16. C42×D97 | C4 | semidirect |
| 103. C97 | #1827 | semidirect |
| 108. #339 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095511 | 2 |
| #20260717 | 2 |
| #20260708 | 2 |
| #20260495 | 2 |
| #20260492 | 2 |
| #20260491 | 2 |
| #339×C97 | 2 |
| #1827 | 97 |