Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#13095495 | C2 | semidirect |
| 3. #20260701 | C2 | direct (N × H) |
| 4. C2×#15690722 | C2 | semidirect |
| 5. C23×C8×C97 | C2 | semidirect |
| 15. C2×#13095495 | C22 | semidirect |
| 17. #15690722 | C22 | semidirect |
| 21. C22×C8×C97 | C22 | semidirect |
| 91. C2×C97 | #408 | semidirect |
| 96. C97 | C2×#408 | semidirect |
| 99. C23×C8 | D97 | semidirect |
| 116. C22×C8 | C2×D97 | semidirect |
| 188. C2 | #20260701 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095511 | 2 |
| C22×#13095495 | 2 |
| #20260701 | 2 |
| C2×#15690722 | 2 |
| C23×C8×C97 | 2 |
| C2×#408 | 97 |