Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20260517 | C2 | semidirect |
| 4. #20260516 | C2 | semidirect |
| 5. #349×C97 | C2 | semidirect |
| 14. #15690750 | C22 | semidirect |
| 18. M32×C97 | C22 | semidirect |
| 93. D97 | #349 | direct (N × H) |
| 95. C97 | C2×#349 | semidirect |
| 100. #349 | D97 | direct (N × H) |
| 112. M32 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D97 | 2 |
| M32×D97 | 2 |
| #20260517 | 2 |
| #20260516 | 2 |
| #349×C97 | 2 |
| C2×#349 | 97 |