Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1160 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1160 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×C22⋊Dic97 | C2 | semidirect |
| 3. #20260614 | C2 | semidirect |
| 4. #20260612 | C2 | semidirect |
| 5. #20260596 | C2 | semidirect |
| 6. #20260590 | C2 | semidirect |
| 7. C22×C22⋊C4×C97 | C2 | semidirect |
| 11. C22×C22⋊D97 | C4 | semidirect |
| 15. C23×Dic97 | C22 | semidirect |
| 18. C2×C22⋊Dic97 | C22 | semidirect |
| 19. C2×#13095488 | C22 | semidirect |
| 20. #15690717 | C22 | semidirect |
| 22. C23×C4×C97 | C22 | semidirect |
| 25. C2×C22⋊C4×C97 | C22 | semidirect |
| 29. C23×D97 | C2×C4 | semidirect |
| 36. C2×C22⋊D97 | C2×C4 | semidirect |
| 37. C2×C22⋊D97 | C2×C4 | semidirect |
| 42. C22×Dic97 | C2×C4 | semidirect |
| 66. C23×C97 | C22⋊C4 | semidirect |
| 131. C97 | #2308 | semidirect |
| 134. C22×C22⋊C4 | D97 | semidirect |
| 148. C23×C4 | C2×D97 | semidirect |
| 155. C2×C22⋊C4 | C2×D97 | semidirect |
| 205. C23 | #13095488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D97 | 2 |
| C22×C22⋊Dic97 | 2 |
| #20260614 | 2 |
| #20260612 | 2 |
| #20260596 | 2 |
| #20260590 | 2 |
| C22×C22⋊C4×C97 | 2 |
| #2308 | 97 |