Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#15690742 | C2 | semidirect |
| 3. C2×#15690735 | C2 | semidirect |
| 5. #20260641 | C2 | semidirect |
| 7. C2×C4×C8×C97 | C2 | semidirect |
| 12. C2×#13095500 | C4 | semidirect |
| 64. C2×C4×C97 | SD16 | semidirect |
| 87. C8×C97 | C22⋊C4 | semidirect |
| 113. C97 | #1968 | semidirect |
| 118. C2×C4×C8 | D97 | semidirect |
| 192. C2×C4 | #13095500 | semidirect |
| 200. C8 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| C2×#15690742 | 2 |
| C2×#15690735 | 2 |
| C2×#15690732 | 2 |
| #20260641 | 2 |
| #20260637 | 2 |
| C2×C4×C8×C97 | 2 |
| #1968 | 97 |