Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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. M32×D97 | C2 | semidirect |
| 3. #108×D97 | C2 | semidirect |
| 4. #20260549 | C2 | semidirect |
| 5. #20260548 | C2 | semidirect |
| 6. #20260547 | C2 | semidirect |
| 7. #361×C97 | C2 | semidirect |
| 17. #15690750 | C22 | semidirect |
| 20. #15690746 | C22 | semidirect |
| 23. M32×C97 | C22 | semidirect |
| 24. #108×C97 | C22 | semidirect |
| 95. D97 | #361 | direct (N × H) |
| 97. C97 | C2×#361 | semidirect |
| 104. #361 | D97 | direct (N × H) |
| 117. M32 | C2×D97 | semidirect |
| 121. #108 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D97 | 2 |
| M32×D97 | 2 |
| #108×D97 | 2 |
| #20260549 | 2 |
| #20260548 | 2 |
| #20260547 | 2 |
| #361×C97 | 2 |
| C2×#361 | 97 |