Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
928 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 237 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×C4×D388 | C2 | semidirect |
| 3. #20260641 | C2 | semidirect |
| 4. #20260611 | C2 | semidirect |
| 5. #20260597 | C2 | semidirect |
| 6. #20260595 | C2 | semidirect |
| 7. #95×D97 | C2 | semidirect |
| 8. C4×C22⋊C4×C97 | C2 | semidirect |
| 10. C2×#13095511 | C4 | semidirect |
| 31. C2×Dic194 | C2×C4 | semidirect |
| 35. C2×C22⋊D97 | C2×C4 | semidirect |
| 42. C2×C4×D97 | C2×C4 | semidirect |
| 48. C22×C4×C97 | C2×C4 | semidirect |
| 76. C2×C4×C97 | #41 | semidirect |
| 83. D388 | C22⋊C4 | semidirect |
| 116. C97 | #2339 | semidirect |
| 123. C4×C22⋊C4 | D97 | semidirect |
| 161. C22×C4 | C4×D97 | semidirect |
| 202. C2×C4 | #13095511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095511 | 2 |
| C2×C4×D388 | 2 |
| #20260641 | 2 |
| #20260611 | 2 |
| #20260597 | 2 |
| #20260595 | 2 |
| #95×D97 | 2 |
| C4×C22⋊C4×C97 | 2 |
| #2339 | 97 |