Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#13095496 | C2 | semidirect |
| 2. C2×#15690731 | C2 | semidirect |
| 3. #20260637 | C2 | semidirect |
| 4. #20260490 | C2 | semidirect |
| 5. C2×#127×C97 | C2 | semidirect |
| 22. C2×D388 | D4 | semidirect |
| 27. C2×#11715895 | D4 | semidirect |
| 61. C2×C4×C97 | D8 | semidirect |
| 98. C97 | #2011 | semidirect |
| 100. C2×#127 | D97 | semidirect |
| 163. C2×C4 | #13095496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095496 | 2 |
| C2×#15690731 | 2 |
| #20260637 | 2 |
| #20260490 | 2 |
| C2×#127×C97 | 2 |
| #2011 | 97 |