Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 3. C2×#15690721 | C2 | semidirect |
| 4. #20260497 | C2 | semidirect |
| 5. C4×C4⋊C4×C97 | C2 | semidirect |
| 10. C4×D388 | C4 | semidirect |
| 13. #15690730 | C4 | semidirect |
| 29. C2×#11715895 | C2×C4 | semidirect |
| 38. C4⋊C4×C97 | C2×C4 | semidirect |
| 64. D388 | C42 | semidirect |
| 91. C97 | #1762 | semidirect |
| 95. C4×C4⋊C4 | D97 | semidirect |
| 128. C4⋊C4 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| C2×#15690730 | 2 |
| C2×#15690721 | 2 |
| #20260497 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #1762 | 97 |