Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 152 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. #20261660 | C2 | semidirect |
| 4. #20261659 | C2 | semidirect |
| 14. #15690750 | C4 | semidirect |
| 16. C16×D97 | C4 | semidirect |
| 17. M32×C97 | C4 | semidirect |
| 31. #13095486 | C2×C4 | semidirect |
| 33. C16×C97 | C2×C4 | semidirect |
| 61. D97 | #365 | semidirect |
| 63. C97 | C2×#365 | semidirect |
| 74. M32 | #87604 | semidirect |
| 96. C16 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D97⋊#108 | 2 |
| C2×#15690878 | 2 |
| #20261660 | 2 |
| #20261659 | 2 |
| M32×D97 | 2 |
| C2×#365 | 97 |