Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
3464 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 354 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 |
|---|---|---|
| 1. C22×C22⋊#87604 | C2 | semidirect |
| 2. #20261676 | C2 | direct (N × H) |
| 4. C23×#87604 | C22 | semidirect |
| 6. C2×C22⋊#87604 | C22 | semidirect |
| 8. C24×D97 | C4 | semidirect |
| 9. C24×D97 | C4 | semidirect |
| 12. C25×C97 | C4 | semidirect |
| 14. C22×#87604 | C23 | semidirect |
| 24. C23×D97 | C2×C4 | semidirect |
| 30. C24×C97 | C2×C4 | semidirect |
| 34. C23×C97 | C22⋊C4 | semidirect |
| 46. C22×D97 | C22⋊C4 | semidirect |
| 47. C22×D97 | C22⋊C4 | semidirect |
| 59. C22×C97 | C2×C22⋊C4 | semidirect |
| 67. C2×D97 | C2×C22⋊C4 | semidirect |
| 72. C2×C97 | #379 | semidirect |
| 75. D97 | #379 | semidirect |
| 78. C97 | C2×#379 | semidirect |
| 87. C25 | #87604 | semidirect |
| 105. C24 | C2×#87604 | semidirect |
| 128. C23 | C22⋊#87604 | semidirect |
| 146. C22 | C2×C22⋊#87604 | semidirect |
| 153. C2 | #20261676 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#87604 | 2 |
| #20261676 | 2 |
| C25×D97 | 2 |
| C2×#379 | 97 |