Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
156 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 3. #20261662 | C2 | semidirect |
| 4. #20261661 | C2 | semidirect |
| 14. #15690750 | C4 | semidirect |
| 15. #15690749 | C4 | semidirect |
| 17. M32×C97 | C4 | semidirect |
| 31. #13095486 | C2×C4 | semidirect |
| 33. C16×C97 | C2×C4 | semidirect |
| 67. C97 | #2159 | semidirect |
| 78. M32 | #87604 | semidirect |
| 100. C16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261745 | 2 |
| C2×#15690879 | 2 |
| #20261662 | 2 |
| #20261661 | 2 |
| M32×D97 | 2 |
| #2159 | 97 |