Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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. #20260674 | C2 | semidirect |
| 3. #20260661 | C2 | semidirect |
| 5. #20260646 | C2 | semidirect |
| 6. C4×#13095488 | C2 | semidirect |
| 7. #20260581 | C2 | semidirect |
| 8. C2×C4×Q8×C97 | C2 | semidirect |
| 97. C97 | #2398 | semidirect |
| 98. C2×C4×Q8 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| #20260674 | 2 |
| #20260661 | 2 |
| #20260652 | 2 |
| #20260646 | 2 |
| C4×#13095488 | 2 |
| #20260581 | 2 |
| C2×C4×Q8×C97 | 2 |
| #2398 | 97 |